Embodiments of the present disclosure generally relate to secure communication and/or communication networks, such as use of quantum keys to encrypt communications and/or time-sensitive networks (TSN).
Quantum key distribution (QKD) currently is being investigated for its theoretical ability to distribute random keys between parties for encrypting messages, while simultaneously ensuring that no other party is able to eavesdrop in an undetected way on the key distribution channel. The technique makes use of certain properties of quantum mechanics that prevent a third-party observer from interacting with a system in certain ways without affecting the communication system or network in measurable ways. Time-sensitive networks (TSN) may be required for communication that must be delivered at a specific time, high priority messages, etc. Low priority messages, on the other hand, can be buffered and passed on a best-effort basis, with no timing and delivery guarantees.
One example of a system in which a TSN may be used is a power grid communication network where there are communication network paths that connect devices and may include redundant pathways. Multiple edge devices at various nodes may be included, such as at step-down transformer stations or solar generation stations. These edge devices can be used to monitor temperatures, pressures, or various processes, and which may also require secure communication channels. The nodes typically have substantial infrastructure able to support more complex and expensive instrumentation. In particular, to support high-speed and long-distance QKD communication, cryogenically cooled single-photon detectors preferably may be used. These detectors require substantial electrical power, water cooling, and routine maintenance, and are very expensive (e.g., on the order of $100,000 for a pair of the detectors). As such, these detectors typically may only be placed at a few locations in the communication network. On the other hand, there are many more (e.g., an estimated 400,000) end and edge devices on the power grid, not including solar installations, which can add around another 1.6 million devices.
Enabling encrypted communication among all these devices via QKD necessitates a much lower-cost solution. Furthermore, many of these edge devices may be monitoring and/or controlling critical processes that require TSN. Communications with devices may need to occur at specific times, or if a process monitor finds a problem or failure, the monitor must be able to issue a time-critical alert. At the same time, these monitors or controls must not be spoofed or hacked by some malevolent adversary intent on bringing down the power grid. Therefore, combining QKD with TSN in a manner that enables low-cost, chip-based solutions at the edge devices is needed.
A photonic integrated circuit includes a waveguide configured to receive photons from an optical fiber and direct the photons in a loop formed by the waveguide. The circuit also includes one or more of a variable optical attenuator coupled with the waveguide and configured to adjust a number of the photons between a key level and one or more decoy levels, an intensity modulator coupled with the waveguide and configured to adjust a number of the photons between a key level and a decoy level, and a phase shifter coupled with the waveguide and configured to change a phase of the photons. The waveguide is configured to direct one or more of the photons back out of the optical fiber after the one or more of the photons has passed through the loop formed by the waveguide with a polarization state of the one or more of the photons rotated by 90°.
A method of assembling a photonic integrated circuit includes forming a waveguide configured to receive photons from an optical fiber and direct the photons in a loop formed by the waveguide, and coupling, to the waveguide, one or more of a variable optical attenuator configured to adjust a number of the photons between a key level and one or more decoy levels, an intensity modulator configured to adjust a number of the photons between a key level and a decoy level, or a phase shifter configured to change a phase of the photons, wherein the waveguide is configured to direct one or more of the photons back out of the optical fiber after the one or more of the photons has passed through the loop formed by the waveguide with a polarization state of the one or more of the photons rotated by 90°.
The subject matter described herein will be better understood from reading the following description of non-limiting embodiments, with reference to the attached drawings, wherein below:
Alice and Bob may attempt to establish a secure communication channel between Alice and Bob via the network for secure communication of signals. A third-party computing device (referred to as “Eve” and may be similar or identical to Alice and Bob except under the control and/or direction of a third party) may be trying to eavesdrop on the channel between Alice and Bob. Another computing device (referred to as “Charlie”) also may be part of the communication channel between Alice and Bob but is not necessarily a trusted part of the channel. Alice and Bob may each be separately communicatively coupled with Charlie via optical fibers. For example, Alice may not be disposed along the optical fiber(s) between Bob and Charlie, and Bob may not be disposed along the optical fiber(s) between Alice and Charlie.
Plug-and-play in a QKD approach can allow for the components required at either Alice and/or Bob to be relatively inexpensive compared to currently known components. In particular, plug-and-play can eliminate the need for light detectors and light sources at one end of the channel by placing the detectors and light sources at Charlie's node in between Alice and Bob. If Alice and Bob are edge devices, then Charlie can be an untrusted central node connected to many edge devices.
In this design, Bob generates light pulses and sends the light pulses through Mach-Zehnder interferometers (M-Z1 and M-Z2). As a result, there are three output pulses. One pulse propagates through both short arms of the interferometer, one pulse through both long arms, and a third pulse which propagates through either of the two short-long arm paths. A phase of shift of 2π/3 in the long arm of one interferometer ensures that when these two photon paths recombine and interfere, the resulting photon amplitude is equal to that of the other two pulses. Alice attenuates the pulses to less than a single photon level on average and applies a random phase shift of π/3 or 4π/3 to the first pulse, and 0 or π to the third pulse. No phase shift is applied to the second pulse. On the return path at Bob, the arm lengths of M-Z2 are chosen so that the second pulse traveling through the short arm of the interferometer interferes with the first pulse traveling through the long arm. Similarly, the third pulse traveling through the short arm interferes with the second pulse traveling through the long arm. As a result, only four pulses emerge on the return path from M-Z2. The pulses are then shunted into two detectors before reaching M-Z1. Due to the phase shifts applied to the pulses, the two center pulses will split between detectors 1 and 2 (DET1 and DET2) at Bob. Bob knows which detector has measured a photon, while Alice knows which random phase shifts were applied by Alice and so Alice can predict or otherwise determine which of Bob's detectors will respond for each pulse. In this way, a random key can be exchanged between Alice and Bob without Alice needing detectors or light sources.
This design may be able to be integrated into a computer chip for Alice, but not for Bob because the interferometers which require lengths of fiber in the short and long arms of the interferometers are at Bob's end. Alice has a Faraday rotator to eliminate effects of birefringence in the fiber channel, but this can be accomplished on-chip without need for a Faraday reflector as described below. However, the system design at Bob's end is complex. The two interferometers must be tightly matched, which means extremely good temperature control of the fiber arms as well as feedback systems to constantly maintain the interferometer arm lengths.
Another QKD technique combines both the measurement device independence and the plug-and-play benefit. But, for MDI-QKD to work, the photons prepared by Alice and Bob may need to be identical in time, wavelength, and polarization when the photons reach a non-polarizing beam splitter (NPBS) of Charlie. In practice, this is challenging and may not be easily implemented within a photonic integrated circuit or chip (PIC). Sometimes lasers are frequency-locked using gas cells. Other times, distributed feedback (DFB) lasers are continuously adjusted with temperature controllers. Drifts in photon polarization and arrival times also may need to be continuously monitored and actively controlled with instruments that are usually large and expensive. Over long lengths (e.g., twenty kilometers (km) or longer) of fiber, the travel time of an optical pulse can drift by up to thirty nanoseconds (ns).
With respect to Charlie, that computing device includes a light source 312 (e.g., a laser) that emits a polarized (e.g., vertically polarized) laser light beam (e.g., into an internal optical fiber and/or waveguide of Charlie). A non-polarizing beam splitter (NPBS) 314 of Charlie can be a 50:50 beam splitter that splits the output of the light source 312 into two beams of equal or approximately equal intensity (e.g., intensities within 1% of each other) that can be independently modulated by separate intensity modulators 316, 318 of Charlie. For example, the modulators 316, 318 can separately modulate the beams into three ns pulses at one megahertz (MHz) (or pulses of another duration and/or other frequency) and with variable time delays between the pulses sent to Alice vs. the pulses sent to Bob.
A half waveplate (HWP) 320 in Charlie rotates the polarization state of one beam (e.g., the beam exiting the modulator 318) to be orthogonal to the other beam (e.g., the beam exiting the modulator 316). These two beams are then recombined by a polarizing beam splitter (PBS) 322. The recombined beams then enter an asymmetric Michelson interferometer 324 having one arm 326 that is much longer than the other arm 328 of the interferometer 324.
A NPBS 330 evenly splits the recombined beams into the two arms of the interferometer 324. The lengths of the arms 326, 328 can be adjusted to return the pulses so that the pulses are separated in time by a designated or fixed time period (e.g., one hundred ns or another time period). Using a free space Michelson interferometer 324 with polarization multiplexing instead of a Mach-Zehnder interferometer with a fiber delay as in one or more other designs allows for the time separation between the pulses to be identical and relatively unaffected by thermal drifts. A PBS 332 then re-splits the two polarizations of the recombined beam and sends one pulse train to Alice and the other to Bob. Another HWP 334 is inserted in the beam sent toward Bob so that the polarization state of the pulse train sent to Bob is identical to the pulse train sent to Alice. This can ensure that the beam passes through another PBS 336 and into the fiber cable 308 toward Bob.
Encoding of the pulse stream by Alice and Bob is handled by intensity and phase modulators of the PICs 310 of Alice and Bob, as described below. The intensity modulators only affect the return pulses and are used to randomly select or block either the first or second pulse. The phase modulators randomly adjust the phase of each pulse to be 0 or π. These are the two bases (time-bin and phase) used for encoding. The PICs 310 of Alice and Bob have a variable attenuator that can ensure the return pulses have on average a fraction of a photon except for decoy states.
While only the photonic components of the PIC 310 are shown in
The PIC 310 includes a waveguide 406 (e.g., an internal optical fiber) that forms a raceway or loop in or on the PIC 310. The waveguide 406 is coupled with the external fiber 308 by a polarizing beamsplitter/polarization rotator (PBS/PR) 420. Arrows 408 in
The photon received into the waveguide 406 in the PIC 310 from the beamsplitter 402 may have a horizontal polarization. The photon encounters one of the taps 410 (e.g., the tap 410 on the left side of the PIC 310 in
The VOA 414 reduces the light level (e.g., the brightness, intensity, or the like) so that, during key generation, the PIC 310 is unlikely to emit more than one photon. The light is then received by an intensity modulator 416 that adjusts the average number of photons between a key level and decoy level(s). A phase shifter 418 (“φ-shifter” in
Because of the polarizing beamsplitter/polarization rotator 420 combination at the entrance of the PIC 310, the returning photon has had its x/y polarization components interchanged as occurs in a Faraday mirror so that, after the photon returns to Charlie through the fiber cable 308, the effect of birefringence is eliminated. When the photon reaches Charlie (as shown in
In one embodiment, a communication network that includes Alice, Bob, Charlie, and other nodes can be integrated with TSN.
Best effort communications may be communicated within the TSN 500 when there is sufficient bandwidth in the TSN 500 to allow for the communications to be successfully completed without decreasing the available bandwidth in the TSN 500 below a bandwidth threshold needed for the communication of time sensitive communications between devices. The communication of best effort communications may be delayed, ensuring that the time sensitive communications are not delayed. Rate constrained communications are communications that are communicated using the remaining amount of bandwidth, if any, in the network. For example, a rate constrained communication may be sent between devices using the bandwidth in the network that is not used by the time sensitive communications and the best effort communications. If no bandwidth is available (e.g., the time sensitive and best effort communications consume all the available bandwidth), then the rate constrained communication may not occur until more bandwidth is available.
As previously described, the QKD technique using Charlie 306, Alice 302, and Bob 304 places the expensive, power hungry equipment (including the light source and detectors) at Charlie, which may be an untrusted node. This node may be connected to multiple edge devices or a control center that is connected to multiple stations. Ideally there are very few of the Charlie nodes on the network due to the complexity, expense, and required routine maintenance for these types of nodes. The approach described above in connection with the system 300 can solve the problem of laser wavelength control. The laser source can be a low-cost DFB laser diode which is temperature controlled to maintain a fixed wavelength over the time interval corresponding to the difference in arrival times of the photons from Alice and Bob. For example, if the optical fiber length from Charlie to Alice is ten km longer than the length of the optical fiber from Charlie to Bob, this corresponds to a time difference for photon travel of around fifty microseconds, or a round-trip time difference of one hundred microseconds.
So long as Charlie's laser temperature and wavelength remains sufficiently constant over this very short time interval to within the bandwidth of the laser line, the photons from Alice and Bob will be indistinguishable in wavelength after returning to Charlie. By using Faraday mirrors and a time-bin/phase encoding technique, the distinguishability between the two photons from the polarization effects of the fiber birefringence can be eliminated. The only remaining issue is a requirement that the photons from Alice and Bob photon return to the NPBS 330 of Charlie at the same instant. Stated differently, the photon wavefunctions from Alice and Bob must overlap when they arrive at the beamsplitter 330.
A network configurator (NC) 502, or alternatively, centralized network configurator (CNC), manages and controls the entire network. The CNC can have complete information about network topology. Topology information can be manually entered or devices on the network 500 (end-systems 302, 304, 504, switches 506, and/or routers 512) can report information about the immediately adjacent connections (neighbors), thereby enabling the entire interconnectivity of the network 500 to be discovered by the CNC 502. This includes both classical (e.g., Ethernet or wireless) devices and connections as well as quantum optical devices and connections. For example, communication links 508 shown in
The CNC can use QKD-generated keys to authenticate and encrypt communication with devices in or on the network. For the classical control plane (e.g., communication via wired and/or electromagnetic wireless communications), the maximum size of every message is known, a priori, by the CNC, where message size is used to compute message transmission time. For the quantum data plane (e.g., communications using transmission of light via or along optical fibers), a single-photon message size can be the duration of time between the request for transmission of a single photon and the time the photon is actually emitted by the device. For a classical system, this can be known with a high degree of determinism, but for a quantum system, a Poisson mean value may be the most that can be determined.
The propagation delay along every link 508 may be known a priori, inferred either via cable length or via a variety of means that involve echoing a small message from adjacent neighbors 302, 304, 306, 504, 506. The CNC can query optical components within the network 500 for the single-photon propagation delay of quantum fiber channels 508.
A separate time synchronization protocol, for example, one of the many profiles (variants) of Precision Time Protocol (PTP), known as gPTP, maintains clock synchronization throughout the network 508. This can be accomplished by ensuring network interfaces support hardware timestamping, enabling accurate and precise timestamps that are placed in short messages exchanged to measure link delay. Timestamping is done within the hardware as close to the “wire”, e.g. the physical link, as possible to ensure no jitter or delay occurs from anything other than propagation time over the link. Typically, messages are sent and returned with appropriate timestamps allowing the device 302, 304, 306, 504, 506 initiating the propagation delay measurement to divide by two assuming the link is symmetric. Propagation delay measurements can be periodically performed to ensure up-to-date results.
Once link propagation delays are known, synchronization messages are exchanged between devices 302, 304, 306, 504, 506 that contain the current clock tick rate. The devices 302, 304, 306, 504, 506 may include or be connected with separate clocks, with one of the clocks identified or selected (e.g., by the NC 502) as a grandmaster clock and all other clocks adjust their tick rate ratio such that the time of the other clocks matches the notion of time of the grandmaster clock. Since clocks are clearly defined relative to one another in a master-slave relationship forming a spanning tree, clock rates are adjusted relative to one another such that all clocks match the grandmaster clock. Stated differently, grandmaster time can be reconstructed by every clock in the network 508. There may be some error, however small, typically measured in root mean square (RMS) nanoseconds. This error can be dependent upon the stability of the clocks, how often the synchronization messages are sent, and in a large network 508, on placement or selection of the grandmaster clock within the network topology relative to the other clocks.
All of the PTP message exchanges can be authenticated and encrypted using QKD-generated keys, as described above. The network 508 is time synchronized, and the CNC 502 knows message sizes, the network topology, and link propagation delays. The CNC 502 also knows the source and destination of messages in the network, including classical control messages and quantum data plane messages. If the CNC 502 is provided with maximum-tolerated latencies for each pair of end-systems that need to communicate (e.g., the devices 302, 304, 306, 504), the CNC 502 can determine a single-photon path and schedule when each device (e.g., nodes 506, which can represent switches) along the path should transmit the photon. The CNC 502 can compute initial transmission (photon emission) and periodic opening and closing times of gates (the switches 506) for each device 302, 304, 306, 504 along a network path (e.g., the links and switches between and interconnecting communicating devices) such that messages are sent and received at precise, periodic intervals forming a connected path while simultaneously avoiding collision within the network 500. Collision occurs when transmitting more than one message at the same time (such that the photons, in this case, would overlap) over the same link 508.
However, as described above, there are quantum networking algorithms where the goal is to create a perfect collision, namely a simultaneous event where two messages (single photons) arrive at the same location at the same time. And the goal is to accomplish this simultaneous event periodically. Although this is something a network scheduler 510 typically seeks to avoid, it is an interesting task to add to the capabilities of the scheduler 510. The scheduler 510 can represent a computing device that schedules when different switches 506 are open, when different devices 302, 304, 306, 504 communicate in the network 500, and the like.
In a classical setting, the CNC 502 attempts to meet or exceed the required minimum latencies for each deterministic flow of data. This can be tightened to provide exact latencies. Also note, that in a strictly classical Ethernet setting, the CNC 502 can control the flow of a classical data plane. However, the control plane can remain classical, while the data plane is quantum. The CNC 502 can send configuration information to configure known, deterministic paths through the quantum data plane at precisely periodic time intervals. Typically, this would be done via a YANG module that exposes network configuration and control information about a device. The CNC 502 can either be provided with the required quantum channel paths or be able to query and learn about the quantum network via NETCONG/YANG or Link Layer Discovery Protocol (LLDP), and infer when specific quantum channel paths are required. For example, if the CNC 502 were provided with the fact that certain network devices 302, 304, 306 identified themselves as Alice, Bob, or Charlie, and the duration of time connections are required among Alice, Bob, and Charlie, then the CNC 502 can compute and configure such connectivity for the entire network 500. The CNC 502 can decide as to which Alice, Bob, and Charlie combinations are optimal for the network 500, depending upon the locations, capabilities, and QKD key consumption requirements within the network 500.
Since the network is time synchronized, the CNC 502 also can provide meaningful information about whether, and precisely when, a coincidence event happened at Charlie to Alice and Bob, and can provide additional support and verification of events needed for MDI-QKD. There exist numerous scheduling algorithms that can be used by the CNC 502. We anticipate the CNC becoming a quantum algorithm running on a quantum computer within the quantum network.
If Alice and Bob are edge devices that are part of a TSN 500, then the node (e.g. Alice, Bob, or Charlie) includes a network clock. Each network output port has a clock in TSN 500 to control the gates. The clocks on the devices can be synced to network time (e.g., the grandmaster clock). A QKD chip can use this clock for timing. Alice and Bob can use timing, for example, to modulate the pulses from Charlie, determining which pulses to shutter or pass, which pulses to phase shift or not phase shift, and which pulses are decoy states that have a different average number of photons.
Another interesting difference between classical use of the CNC 502 and the inventive subject matter described herein is that classically, the CNC 502 computes a single cycle time with offsets indicating when each network event occurs, and this cycle time and these offsets remain constant over many cycles. In one embodiment of the inventive subject matter, however, propagation delays may need to be updated more often due to sensitivity of fiber length on propagation delay. It is recognized that re-computation may only be done when propagation delay changes are significant enough to warrant a re-computation. This could be determined, for example, by a noticeable drop in the key production rate. It should also be noted that the CNC 502 can now control events such as coincidence detection windows and photon detector gating as well as network switches 506 and classical Qbv gate control.
The CNC 502 can direct Charlie when to send an initial calibration pulse to both Alice and Bob and configure the network switches 506 such that the pulse travels to Alice and Bob and back to Charlie so that Charlie can then determine the correct time delay, report the time delay back to the CNC 502, and the CNC 502 can tell Charlie again when to send the QKD pulse sequence to Alice and when to send the QKD pulse sequence to Bob, while ensuring that the appropriate network paths are selected.
Alternatively, if Alice's, Bob's, and Charlie's clocks are synchronized, then Alice and Bob only need to timestamp when each received Charlie's pulse, and report the timestamps to the CNC 502. Charlie can report when the pulse was sent by Charlie (can report to the CNC 502). The CNC 502 can then tell Charlie when to send the QKD pulses to Alice and Bob and also when to expect the return coincidence from Alice and Bob. Charlie may need to gate the detectors 338, 340 to just look for the return photon coincidences from Alice and Bob within a narrow time window to eliminate dark count noise from the detectors 338, 340.
Since Charlie can be assumed to be untrusted, consideration can be made regarding what capabilities are placed on Charlie. For example, Charlie may be prohibited (e.g., by the CNC 502) from being a grandmaster clock. As another example, Charlie may not be included (by the CNC 502) in the time synchronization and scheduling processes described above, as Alice and Bob (which are trusted nodes) can participate in time synchronization and scheduling without Charlie. However, if Charlie were to attempt to report misleading values, this would fail to create simultaneous events leading to detectable error.
As shown in
When a regularly scheduled communication is to take place between two devices, the TSN scheduler 510, which may be collocated with Charlie, fixes the route for the communication and directs Charlie to determine the optical time delay between Charlie and Alice, and between Charlie and Bob, by sending a classical (e.g., high intensity, many photon) pulse from the QKD laser of Charlie over the channel along the route. Charlie also can send a several photon pulse during the QKD process described above as well, so this classical pulse may not require modification of the laser pulse intensity of Charlie. The TSN scheduler 510 can direct the appropriate switches 506 are open along the route so that the pulse is not intercepted and buffered at any switch 506. Alice and Bob reflect the pulse back to Charlie along the same route, as described above.
Stated differently, Alice and Bob may not attenuate the pulse from Charlie to single photon levels like Alice and Bob do during the QKD process described above. Alice and Bob may still return the pulse (via Faraday mirrors or the waveguides 406) to reflect the pulse so that time delays from fiber birefringence are also included in exactly the same manner as during the QKD process described above. Charlie still distinguishes between return pulses from Alice and Bob. If the return pulses are polarized identically, as the pulses are for the PICs 310 described above, then Charlie may insert another splitter in the return path for Alice and Bob to detect each return pulse separately. Because the pulses are relatively bright pulses, the splitters may not have to split off much light to separate conventional photodetectors. Alternatively, in schemes in which the return pulses arrive oppositely polarized, because the pulses will arrive at different times, the pulses may be distinguishable and identifiable at the single photon detectors 338, 340. Detecting the pulses with the built-in single photon detectors 338, 340 can automatically include timing delays from the detectors 338, 340. Alice and Bob may still need to attenuate the return pulses so that the return pulses do not saturate the detectors 338, 340. Instead of a single pulse, Bob may also send a pulse sequence to Alice and Bob to provide better timing information from weak return pulses.
Charlie can determine the time difference between detection of the two pulses and can communicate this time difference to the TSN scheduler 510. The TSN scheduler 510 can select the same route and opens the channel for the QKD key distribution to Alice and Bob at the appropriate times (which may be different depending on the time delay required). Charlie now knows the delay that should be used between the photon sent from Charlie to Alice and the photon sent from Charlie to Bob so that the reflected photons arrive at the NPBS 330 at the same instant. When triggered by the TSN scheduler 510, Charlie then can send the sequence of pulses to both Alice and Bob with the appropriate delay. The TSN scheduler 510 can set up this time calibration routine as frequently as required so that the slow drifts in the speed of light over the optical fibers that occur do not affect the quantum key distribution.
The network scheduler 510 can configure QKD data transfer from Alice and Bob over two different quantum channels of different lengths such that the quantum data arrive simultaneously at Charlie. The network scheduler 510 can determine the time delay for data that is sent between Charlie and each of Alice and Bob. While the control plane is classical, the data plane is a separate quantum channel that may need to interoperate with the classical scheduler 510, and requirements for data transfer and synchronization across the separate quantum channels are different than for a classical channel (e.g., in the quantum channel, single photons are being transferred and the photons must be indistinguishable when they arrive at Charlie for Charlie to make a valid measurement; the photons must arrive with the same polarization, same wavelength, and at the same time).
In one embodiment, this can be achieved by Charlie sending a pulse along a specific network path to both Alice and Bob, and report the absolute time (e.g., 22:01:33.846) to the scheduler 510. This time can be when Charlie emitted the pulse. Alice and Bob also can individually report (to the scheduler 510) the absolute time at which each received the respective pulse. Charlie's, Alice's and Bob's clocks can be synchronized to the grandmaster clock with precision so that a time delay between the two round trip pulses through Alice and Bob can be accurately calculated by the scheduler 510. The scheduler can make additional corrections for latency in the electronics of the devices 302, 304, 506, 508, or other factors.
In another embodiment, Charlie can send a pulse along specific network paths to Alice and Bob. Alice and Bob can return the pulse along the same network paths to Charlie without attenuation to low photon levels. Charlie can then determine the elapsed time between sending the pulses and receiving the pulses, and can report the time delay to the scheduler 510 (rather than absolute time). In this case, Charlie could send separate pulses first to Alice and then to Bob to determine their separate propagation times, or Charlie could switch in a photodetector at his node into each fiber connection to Alice and Bob, just send one pulse that is simultaneously split to both Alice and Bob, and then detect the return pulses separately. This approach has the advantage in that absolute timing accuracy is not required. Only Charlie needs to make a time measurement, and he only needs to make a measurement of the time delay between the two return pulses. Again, either Charlie or the scheduler may need to make small corrections to the time delay to account for electronics latency.
The scheduler 510 can provide a network path from one node 506, 512 to two different devices 302, 304, 306, 504 such that light pulses from Charlie are emitted at appropriate times along the two different network paths to Alice and Bob, and then return to Charlie at the same time. In one embodiment, this can occur by adding a constraint to the scheduler 510 that two data flows must arrive at the same destination at the same absolute time. In this case, the flow from Charlie to Alice may be opened at a different time than the flow from Charlie to Bob, even though the network path for the return pulses to Charlie may close at the same time when the data transfer is complete. In another embodiment, a single Alice, Charlie, and Bob flow can be created for the duration required and then divide the flow into Alice-Charlie and Bob-Charlie portions as a separate step.
The network scheduler 510 can determine how to configure a large pool of devices, each identifying as an Alice, Bob, or Charlie throughout the network 500. This could include finding the shortest network path to reduce optical attenuation. The scheduler 510 can communicate with either (a) Charlie or (b) Alice and Bob so that Charlie, or Alice and Bob, can adjust attenuation settings depending on the length and optical losses of the selected network path so that the devices are communicating at the appropriate fractional photon level for the QKD and decoy states.
Alice and Bob can determine when Alice and Bob receive pulses from Charlie to modify those pulses by phase shifting, attenuation, etc. This knowledge can come directly from Charlie with some initial classical communication before subsequent QKD pulses, for example, or the scheduler 510 can communicate with Alice and Bob in a classical manner (e.g., through Charlie). Alice and Bob have built-in clocks synchronized to the grandmaster clock, which can enable Alice and Bob to modulate the pulses from Charlie at the appropriate times once Alice and Bob know when the pulse data stream is arriving. Alice and Bob also can have some type of randomizer for selecting phase shifts, time-bin attenuations, decoy state amplitudes, etc.
After completion of the quantum pulse sequence, Charlie can broadcast the results of Bell state measurements to both Alice and Bob over the classical channel, Alice and Bob can share the random bases they selected for each pulse over the classical channel, and Alice and Bob in turn can compute the error rates and private key(s) (e.g., using processors of Alice and Bob).
The following provides additional information on one or more embodiments of the inventive subject matter described herein.
Three tasks of the Time Sensitive Quantum Key Distribution (TS-QKD) program are focused on chip integration. This document summarizes the results of Task 9, “Identify technologies for implementing integrated QKD chip architectures and filling identified gaps via analysis, simulation, and/or experimentation as appropriate, and architecture.” It builds upon Task 7, “Prepare integrated architectures and identify technology gaps in support of Time-Sensitive QKD supported by analysis, modeling, and experimentation as appropriate” and Task 6, “Develop standard network management QKD data model for configuration and management of Time-Sensitive QKD.”
Chip layouts are shown herein as block diagrams for implementing a QKD system. A chip design suitable for implementation using current technology is proposed for several different network and fiber configurations. This design relies upon and enhances time sensitive networks (TSN) for its operation. A star network approach that maximizes the number of end/edge device connections while minimizing cost through use of chip-level solutions at edge devices is considered in detail.
In this document, we first discuss requirements for the power grid. We explain a hybrid network approach to minimize network cost. Although many different QKD techniques have been developed and discussed in the literature, we focus on measurement device-independent QKD in the third section as an approach in which all the vulnerabilities due to imperfections in detector technology have been eliminated, making this perhaps the most secure practical QKD approach that has been described. Two varieties of MDI-QKD are discussed in detail.
A QKD technique with distinct advantages for integration into photonic integrated circuit (PIC) chips is called “plug-and-play.” We discuss this technique in some detail, followed by a discussion of an approach in which plug-and-play has been successfully integrated with MDI-QKD. The advantages of the combined approach are substantial from both a security standpoint and from a PIC chip implementation standpoint. This section is followed by a QKD network design that minimizes the number of expensive Charlie nodes while enabling PIC chips at all edge devices.
Integrating this proposed chip and network configuration with time-sensitive networks (TSN) is discussed in the next section. It is seen that the QKD chip design and hybrid network design are especially compatible with TSN. In the next section we discuss the actual chip layout for the proposed PIC chip design. This is followed by a short section describing various enhancements to the chip that could ultimately be included along with the components specifically for QKD key transfer such as quantum random number generators. The calculation of the QKD key generation rate follows this section. The calculation for time-bin/phase encoding in the MDI-QKD technique is relatively complex and tedious and is outlined in detail in an appendix. A following section briefly describes the implementation of the chip fabrication. The goals of this task have been fully met with a design for both a chip and a TSN-based QKD network that could be implemented on the power grid.
The goal of Task 9 is to identify technologies for implementing integrated QKD chip architectures and filling identified gaps. A photonic integrated circuit (PIC) chip design that can be fully implemented today to deliver quantum key distribution technology to the power grid in a cost-effective manner is described herein. Furthermore, we describe a network configuration that minimizes the expensive components of the technology and enables quantum encrypted communication between an arbitrary number of edge devices on the power grid. The basic concept makes use of the measurement device-independent technique (MDI-QKD) enhanced by a plug-and-play design. This enables a PIC design in which no light sources or detectors are located at the edge devices but are entirely located at an untrusted node at the center of a star network. This network design is particularly compatible with time-sensitive networks (TSN) as will be discussed in more detail herein.
There are a wide variety of QKD techniques. These techniques are more or less suitable for an integrated photonic chip architecture. It has been estimated that over 200,000 integrated QKD interfaces would be required to fully protect the edge devices on the grid. If limited deployment to end devices is included, the number rises to over 400,000. Including solar installations, the estimated number of required QKD chips is over 2 million. Therefore, to fully protect the power grid by QKD will necessitate a low-cost solution, of which integrated photonic chips will be the only option.
Some of the most important factors that will influence choice of QKD chip design are the distance between communication sites, cost, and required data rates. A generic state-of-the-art grid communication architecture with integrated QKD hardware is shown in
It is likely that to protect the entire power grid with QKD, it will be necessary initially, and perhaps for a long period of time, to combine different types of QKD devices on the network (making QKD standards essential). How this can be done is not yet obvious. For example, at a central trusted node, two or more different and separate QKD stations operating under different protocols (BB88, E92, B92, CV, etc.) and/or with different techniques (entangle photons, single photon, polarization, time-bin/phase shift, etc.) may be co-located and physically connected to an intermediate device to transfer keys between the different QKD systems, thereby enabling key-sharing and classical communication between two devices located on different QKD networks. Alternatively, some work is being done that might enable one system to operate under several different QKD protocols.
It is also clear that different network nodes will have different operating requirements. Some devices may employ cryogenically-cooled detectors, for example, and enable long distance and/or high speed QKD across optical fiber for hundreds of kilometers. These devices will inevitably be large and expensive. They in turn will be connected to local nodes, edge devices, or perhaps even end devices via lower cost, more compact systems, perhaps including integrated photonic chips.
A hybrid network configuration is shown in
Nodes that are separated by distances up to ˜20 km can potentially be connected without cryogenics, using InGaAs detectors, which are still much too expensive for placement at edge devices. Shorter distance links, on the order of 10 km or less may be capable of handling QKD at a wavelength of 850 nm. As shown in
For PICs to be used at edge devices, there are essentially two options. The simplest approach is to completely eliminate light sources and detectors at the edge devices. This is possible through plug-and-play QKD in which the detectors and light sources are all placed on the central node. In
In the Task 7 report it was pointed out that a secure key can be generated between any two nodes connected together via an intermediate trusted node as shown in
It should be noted that no quantum channel is required between the two edge devices. It is only necessary that they be connected via a classical channel which may even be Wi-Fi. In a star network they are already connected via a central node as shown in
Measurement device independent-QKD (S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108 (2012) 130502; P. Zhang et al., “Reference-frame-independent quantum-key-distribution server with a telecom tether for an on-chip client,” Phys. Rev. Lett. 112 (2014) 130501) is one of many specific QKD techniques. It has received considerable attention because it eliminates many of the potential side channel attacks related to imperfections in detectors that are among the most difficult to handle. It also can enable longer distance key distribution. In this approach, both Alice and Bob generate separate single photons at the same wavelength and polarization, and send them across fiber to an intermediate station, Charlie, who performs a Bell-state measurement. Charlie announces the results of the measurement to both Alice and Bob over a classical channel. Even if the measurement is performed in an untrusted location by Eve, she is unable to determine the original state of photons sent by Alice and Bob. However, Alice and Bob can generate a key from their knowledge of the random state they each selected and the result of the Bell state measurement. The untrusted node, Charlie, between Alice and Bob can in principle be the blue node in
For the photons from Alice and Bob to interfere at Charlie's beamsplitter, they must meet three criteria. They must have the same wavelength, the same polarization, and they must arrive at the same time at the BS. (H-K. Lo, M. Curty and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108 (2012) 130503 and H. Semenenko, P. Sibson, A. Hart, M. G. Thompson, J. G. Rarity and C. Erven, “Chip-based measurement-device-independent quantum key distribution,” Optica 7 (2020) 238. Wavelength can be stabilized by a feedback circuit using an atomic absorption line to guarantee that photons emitted by both lasers have the same wavelength. A typical DFB telecom laser diode has a linewidth 1-10 MHz. Ultra-narrow linewidth lasers are also commercially available at telecom wavelengths with linewidths <100 Hz. (M. Żukowski, A. Zeilinger, M. A. Home and A. K. Ekert, “'Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71 (1993) 4287-4290). The center wavelength can be tuned by laser temperature or current (H. Semenenko, P. Sibson, A. Hart, M. G. Thompson, J. G. Rarity and C. Erven, “Chip-based measurement-device-independent quantum key distribution,” Optica 7 (2020) 238). Very tight wavelength control within ˜10 pm is required to maintain high interference visibility as shown in
The overlap of the photon wavefunctions at the BS is determined by the pulse width. A pulse width of 1 ns corresponds to a bandwidth ˜1 GHz. A pulse width of 10 ns corresponds to a bandwidth of ˜100 MHz. The reciprocal pulse width should be about ten times greater than the laser linewidth, so a 10 ns pulse or shorter would work well with DFB lasers. The photons from Alice and Bob then should arrive at Charlie's BS to within about 10% of the pulse width, or within ˜1 ns. TSN is ideally suited for MDI-QKD in this context, because it can open the network channels for Alice and Bob at the appropriate times for their photons to be coincident at Charlie. In other words, a dedicated quantum fiber channel for each edge device to use whenever needed is not required. After the time scheduler selects optical network paths for the photons, then Alice and Bob each send a light pulse to Charlie and send the time at which they sent their pulse to the time scheduler. Charlie measures the photon arrival times and passes those times to the time scheduler. The time scheduler then determines when Alice and Bob must send their QKD photons so that they arrive at Charlie at the same time within about 10% of the pulse width. Of course, this requires clock synchronization between Alice and Bob to within 1 ns or better (H. Semenenko, P. Sibson, A. Hart, M. G. Thompson, J. G. Rarity and C. Erven, “Chip-based measurement-device-independent quantum key distribution,” Optica 7 (2020) 238). We also note that the timing jitter for superconducting nanowire detectors (SNWD) is typically ˜100 ps or less (https://www.thorlabs.com/thorproduct.cfm?partnumber=ULN15PC).
MDI-QKD based on polarization has been successfully implemented using two separate lasers by employing multiple feedback systems (Spec sheet for Quantum Opus superconducting nanowire detectors). The polarization was stabilized through feedback by using a third laser situated at Charlie's setup. The feedback system disabled data collection every 10 s and sent a high intensity pulse for 250 ms to Alice and Bob. They in turn analyzed the light pulses with commercial polarization controllers and used the result to stabilize the polarization state over the fiber channel. In the setup described in this reference, the photon arrival time and laser wavelength are equalized for Alice and Bob by manual adjustment, but in a real-world application there would need to be automated feedback systems to stabilize these parameters as well. The laser wavelength had to be adjusted every 30 minutes to maintain a frequency difference <10 MHz. Photon arrival time was adjusted on a minute basis through a master clock signal from Charlie through a second set of fibers to Alice and Bob. The arrival time difference was kept <30 ps.
It is important to note that weak coherent lasers are not single photon sources even when the pulse intensity is attenuated by Alice and Bob so that the average number of photons in a pulse is <1 before allowing the pulse to return to Charlie. There is always a certain probability of multiple photons remaining in the pulse. This changes the detection statistics in the anti-diagonal/diagonal (AD) polarization basis (A. Rubenok et al., “Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,” Phys. Rev. Lett. 111 (2013) 130501), but does not affect the ability of the technique to generate encrypted keys. In another proof-of-principle experiment, shown in
Prior to beginning key distribution, Charlie calibrated the time interval for sending pulses from Alice and Bob to him. Charlie sent a master clock signal to both Alice and Bob at a different wavelength over the fiber which they in turn used to pulse their lasers. Bob also had an internal timer with which he adjusted the emission time of his pulse so that it arrived at Charlie coincident with Alice's pulse. Furthermore, Charlie's measurements of coincidences had to be properly synchronized (delayed) with respect to Alice's and Bob's photon emission time. Finally, to correct for small wavelength drifts between the two lasers, a separate detector was used to monitor the beat frequency from the interference of a small amount of light split off from each laser. As an alternative to this procedure, it was suggested that a gas cell with an absorption line at the laser wavelength could be used to independently lock the wavelength of each laser. This laser locking technique, however, is not easily incorporated into a PIC.
Another demonstration of polarization-encoded MDI-QKD is described in T. Ferreira da Silva, et al., “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits,” Phys. Rev. A 88 (2013) 052303. The design of the apparatus is shown in
Alice and Bob first use their polarization controllers to align their horizontal polarization axis with Charlie's PBS. Alice also has an electrical polarization controller at her output that is aligned in the horizontal/vertical (HV) polarization basis, so it only affects the right-circular/left-circular (RL) polarizations. Polarization is realigned every hour. The phase modulators, AO modulators and polarization modulators all require randomness obtained from a random number generator. Charlie has an electrical timing delay generator to synchronize the random number generators and the pulse generators. It also is used to ensure that the pulses from Alice and Bob can be independently controlled to 50 ps.
These examples of MDI-QKD illustrate how a few high-speed nodes with more expensive and larger system components can be used to enable QKD communication between many more lower-level nodes that make use of QKD integrated photonic chips without requiring the larger, more expensive components for, or quantum channels between, all edge devices. Such an asymmetric QKD approach has been investigated by several groups (I. Lucio-Martinez et al., “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11 (2009) 095001; G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame and H. Weinfurter, “Design and Evaluation of a Handheld Quantum Key Distribution Sender Module,” IEEE J. Sel. Topics Qu. Electron. 21 (2015) 6600607; and M. Ziebell, M. Persechino, N. Harris, C. Galland, D. Marris-Morini, L. Vivien, E. Diamanti and P. Grangier, “Towards On-Chip Continuous-Variable Quantum Key Distribution, European Qu. Electron. Conf. 4 (2015) JSV-4-2).
While MDI-QKD has important advantages with regard to security by removing the detectors from a potential QKD attack, there are still severe disadvantages from the standpoint of implementation on a TSN-based PIC. The primary problem is ensuring that photons from Alice and Bob are identical and that they arrive at the same instant at Charlie's NPBS. However, we can begin to see why TSN might be useful in implementing MDI-QKD from the standpoint of deterministically scheduling the network path over which the two photons travel. The scheduler could be located at Charlie—perhaps as an algorithm running on this node—that not only determines the network path and when to operate any switches along the path, but who also controls the master clock and tells Alice and Bob when to emit their photons. Another advantage of MDI-QKD is that it effectively doubles the distance over which QKD can be achieved.
Multiple QKD protocols may be employed on the same network. Interoperability between different protocols has been discussed in the literature (T. Länger and G. Lenhart, “ETSI standardization initiative ISG-QKD,” New J. Phys. 11 (2009) 055051), but will be challenging to implement. For example, it is possible to convert time-bin/phase encoding into polarization encoding for very fast readout (T. Länger and G. Lenhart, “ETSI standardization initiative ISG-QKD,” New J. Phys. 11 (2009) 055051). The protocol proposed herein is based upon discrete QKD, involving single photons, and a time-bin/phase shift protocol. Continuous-variable QKD (CV-QKD) may enable chip-based solutions for somewhat longer distances between central nodes, but there is still some question about the security of CV-QKD and it will not be discussed further herein. Furthermore, discrete component systems, as opposed to chip-based systems, are more likely to be required for long distance and/or high speed QKD. Standards will be required for interoperability of QKD systems developed by different manufacturers, and these standards will need to be developed for a variety of QKD systems and protocols.
Various components for QKD systems: detectors, light sources, etc. were discussed in detail in the Task 7 report and will not be repeated here.
Consider the apparatus shown in
where a† is the photon creation operator and the subscripts denote the incident port, and vertical or horizontal polarization. The wavefunction |01, 02denotes the vacuum state at the two input ports.
The transfer relations for the photon creation operators of a photon entering port 1 or 2 and exiting port 3 or 4 of a 50:50 NPBS are (C. Kupchak, et al., “Time-bin to polarization conversion of ultrafast photonic qubits,” Phys. Rev. A 96 (2017) 053812):
Applying these relations to the four Bell states gives
For the first two Bell states, the result in Eq. (7) indicates that both photons arrive at either detectors D1H, D1V, D2H, or D2V but there are never any single photon coincidence counts between different detectors. This is the well-known HOM interference effect (G. Björk and J. Söderholm, “The Dirac-notation in quantum optics,” (2003), available at https://www.kth.se/polopoly_fs/1.263320. 1550156659!/Menu/general/column-content/attachment/Dirac_notation_pm.pdf). This measurement technique cannot distinguish between these two Bell states, which is a well-known principle of linear optics (C. K. Hong, Z. Y. Ou and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59 (1987) 2044). On the other hand, the last two Bell states always generate coincidence counts. The Ψ3 wavefunction will generate a coincidence between detectors on the same output port of the NPBS, while the Ψ4 wavefunction will generate a coincidence between detectors on opposite output ports of the NPBS.
In the MDI-QKD protocol Alice and Bob randomly and independently select the basis and polarization in which they send out their photons. They typically choose between three bases, the horizontal/vertical polarization basis (HV), the diagonal/antidiagonal polarization basis (AD), or the right and left-circularly polarized basis (RL). If they both happen to choose horizontal polarization in the HV basis, then the input polarization state is
which is transformed to the output state
There are no coincidence detection events because both photons emerge from the NPBS still horizontally polarized from either port 3 or port 4. Both photons are either detected by D1H or by D2H. The input two photon state has been projected onto either Bell state Ψ1 or Ψ2. On the other hand, if Alice chooses horizontal polarization and Bob chooses vertical polarization for their photons then
which is transformed to the output state
Half of the time a coincidence is measured between detectors on the same output side of the NPBS and half of the time a coincidence is measured between detectors on opposite sides of the NPBS. Charlie controls the Bell state measurement apparatus and reports to Alice and Bob the results of all his coincidence measurements: that he measured Bell state 3 (same-side coincidence) or Bell state 4 (opposite-side coincidence). Alice and Bob also separately communicate which basis (HV, AD, or RL) they randomly chose for each photon pulse. All other photon pair detection events are discarded. Thus, the only choices of Alice and Bob that need to be considered are shown in Table 1.
From the table, we see that if Alice and Bob choose the HV basis (Rows 1-4) and Charlie reports a coincidence, then Alice and Bob know that they have sent orthogonally polarized photons. On the other hand, if Alice and Bob have both chosen the AD basis or the RL basis, and Charlie reports a Ψ3 coincidence, then they know that they have chosen the same polarization, but if Charlie reports a Ψ4 coincidence, then they know that they have chosen opposite polarizations. Charlie cannot tell which states were initially chosen by Alice and Bob even when he knows that they have chosen the same basis, so Alice and Bob can generate their secure key.
A typical MDI-QKD system design (N. Liitkenhaus, J. Calsamiglia and K.-A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59 (1999) 3295-3300) is shown in
Alice and Bob independently generate single photons by attenuating a coherent laser pulse. They modulate the polarization state in 2 or 3 nonorthogonal bases. They insert decoy states and then they send their photon to Charlie who performs a Bell state measurement and announces the result. Of course, for interference to occur, the photons from Alice and Bob must be “identical” in polarization and arrive at Charlie's beamsplitter at the same “instant.”
The Bell state measurement system in
â1H†→â3H† (3)
â1V†→−i{circumflex over (a)}4V† (4)
â2H†→−i{circumflex over (a)}3H† (5)
â2V†→â4V† (6)
Following the same procedure as before, we generate a table that gives the results when Alice and Bob choose the same basis.
When Charlie detects a coincidence event on opposite sides of the first PBS with the same polarization, he has measured the Ψ1 Bell state. A coincidence on opposite sides of the first PBS with opposite polarizations corresponds to the Ψ2 Bell state. There are no coincidence events for Ψ3 or Ψ4. If Alice and Bob both choose the HV basis, then a coincidence event indicates that they have also chosen the same polarization state. If Alice and Bob choose the DA basis, then a Ψ1 coincidence event indicates that they have chosen the same polarization while a Ψ2 coincidence event indicates that they have chosen opposite polarizations.
Plug-and-play is an interesting QKD approach in which the components required at either Alice or Bob are minimal and relatively inexpensive. In particular, it eliminates the need for detectors and light sources at one end of the channel. An example of a differential phase shift QKD plug-and-play system (C. Zhou et al., “‘Plug and play’ quantum key distribution system with differential phase shift,” Appl. Phys. Lett. 83 (2003) 1692) is shown in
In this design, Bob generates light pulses and sends them through two identical Mach-Zehnder interferometers. As a result, there are three output pulses. One pulse propagates through both short arms of the interferometer, one pulse through both long arms, and a third pulse which propagates through either of the two short-long arm paths. A phase of shift of 2π/3 in the long arm of one interferometer ensures that when these two photon paths recombine and interfere, the resulting photon amplitude is equal to that of the other two pulses. It should be noted that though we are discussing this in terms of light “pulses,” each photon in the pulse is itself entangled into a superposition of the three optical paths by this double interferometer design. Alice attenuates the pulses to a single (entangled) photon level and applies a random phase shift of π/3 or 490 /3 to the first pulse, and 0 or π to the third pulse. No phase shift is applied to the second pulse.
On the return path at Bob, the arm lengths of MZ2 are chosen so that the second pulse traveling through the short arm of the interferometer interferes with the first pulse traveling through the long arm. Similarly, the third pulse traveling through the short arm interferes with the second pulse traveling through the long arm. As a result, only four pulses emerge on the return path from MZ2. The pulses are then shunted into two detectors before reaching MZ1. Due to the phase shifts applied to the pulses, the two center pulses will split between detectors 1 and 2 at Bob. Bob knows which detector has measured a photon, while Alice knows which random phase shifts that she has applied and so she can predict which of Bob's detectors will respond for each pulse. In this way, a random key can be exchanged between Alice and Bob without Alice needing detectors or light sources.
Although it should be possible to integrate this design into a chip for Alice, the system design at Bob's end is complex. Bob's Mach-Zehnder interferometers (MZIs) require lengths of fiber in their short and long arms. The two interferometers must be tightly matched, which means extremely good temperature control of the fiber arms as well as feedback systems to constantly maintain the interferometer arm lengths. If the MZI's can be replaced with free space Michelson interferometers, this stringent temperature control requirement may be somewhat relaxed. Alice has a Faraday rotator to eliminate effects of birefringence in the fiber channel, and, as we will show, this function can be accomplished on-chip. Although the photons make a round trip between Alice and Bob, the distance advantage of MDI-QKD is not lost because the photon beam emitted from Bob is a bright, many photon beam. It is only on the return trip that Alice has attenuated the beam to less than one photon on average per pulse that restricts the channel distance. Bob can be located at a central hub of a star network as in
It should be noted that the QKD technique illustrated in
By choosing this value for the phase shift θ, the interference between the two pulses at the middle time frame causes the amplitude of all three pulses to be equal. A light intensity feedback system was used to continually adjust the phase shift at Bob's system to ensure pulse amplitude equality.
Alice attenuates the reflected pulses to the single photon level and she applies a random phase shift of π/3 or 4π/3 to the first pulse, leaves the second pulse unchanged, and applies a random phase shift of π/3 or 4π/3 to the third pulse (C. Zhou et al., “‘Plug and play’ quantum key distribution system with differential phase shift,” Appl. Phys. Lett. 83 (2003) 1692). When the returning photon reaches Bob, it passes through only the first MZI and the two outputs of the MZI are then directed to two detectors. The MZI has the effect of converting the three different pulse times into four time bins. It is the center two time bins that involve interference with Alice's applied phase shift. The results for these two time bins are shown in Table 3.
Bob reports to Alice (even on an unsecure channel) in which time bin he recorded a detection event. Bob does not report which detector measured the event, but Alice knows which phase shift she applied, and Bob knows which detector clicked, so they each can then proceed to generate the secret key.
A more interesting QKD technique combines both measurement device independence and plug-and-play (Note: the original paper claims that Alice should apply a phase shift of 0 or π to the third pulse, not π/3 or 4π/3. However, this phase shift does not seem to provide the desired 0 or π relative phase shift to the second pulse; F. Xu, “Measurement-device-independent quantum communication with an untrusted source,” Phys. Rev. A 92 (2015) 012333). As previously noted, for MDI-QKD to work, the photons prepared by Alice and Bob must be identical in time, wavelength, and polarization when they reach Charlie's NPBS. In practice this is challenging and is not easily implemented within a PIC. Sometimes lasers are frequency-locked using gas cells. Other times, DFB lasers are continuously adjusted with temperature controllers. Drifts in photon polarization and arrival times must also be continuously monitored and actively controlled with instruments that are usually large and expensive. Over 20 km of fiber, the travel time of an optical pulse can drift by up to 30 ns (Y. Choi et al., “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93 (2016) 032319). An obvious solution to the problem of wavelength control is for a single light source to be located at Charlie's node so that the same source generates the photons for both Alice and Bob. A block diagram of this system is shown in
A specific implementation of P&P MDI_QKD discussed in C. Zhou et al., “‘Plug and play’ quantum key distribution system with differential phase shift,” Appl. Phys. Lett. 83 (2003) 1692 is shown in
There are some important features of this design. The light source is a continuous (CW) laser. Typically, this may be a diode laser as shown here because these are low cost and can operate in the telecom band, but it could be any other type of CW laser source including gas lasers, solid-state lasers, frequency-doubled lasers, etc. A PBS splits the output to provide an “a” pulse for Alice and a “b” pulse for Bob. Separate intensity modulators are used, one to generate pulses for Alice and one for Bob, to achieve perfect timing between the pulses so that they coincide upon return to Charlie's detectors. The emission times of the pulses are controlled by Charlie who has previously determined the round-trip travel times of light pulses to Alice and Bob. In general, IM1 and IM2 will emit pulses at very different times depending on the total fiber path length between Charlie and Alice or Bob. A single laser is used to send one pulse to Alice and one to Bob at two separate times to ensure that the emitted photons have the same wavelength. Half waveplates (HWP) are used to recombine the two pulses at another PBS. Two NPBS's are used to create an unbalanced MZI for the time-shift encoding, thereby splitting each pulse into two pulses (or more accurately, each photon in the pulse becomes entangled in two separate time-bins) and finally another PBS again splits the “a” and “b” pulses for Alice and Bob, respectively. Alice and Bob receive the relatively high-power pulses from Charlie and immediately split off a portion of each pulse to generate timing information and protect against bright light attacks from Eve. They each then use an intensity modulator to reduce the photon number in the return pulse to <1, a phase modulator that randomly time-shifts the phase between the pulse pair by 0 or π, and a Faraday rotator to return the photon in the orthogonal polarization. A photon entangled between the two time-bins in the phase shift basis can be represented as
where ϕ is the relative phase shift between the pulses in bin 1 and bin 2. For the two phase shift states {0,π}, this corresponds to replacing the eiϕ factor by ±1.
The return photons are split off by PBS's and interfered by Charlie in a Bell state measurement. It should be noted that there is also a phase randomizer at both Alice and Bob to ensure that there is no remaining coherence from Charlie's laser between Alice's and Bob's photon, which can in principle make the channel susceptible to an “unambiguous state discrimination” eavesdropping attack (D. Stucki et al., “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys. 13 (2011) 123001; C. H. Park et al., “Practical plug-and-play measurement-device-independent quantum key distribution with polarization division multiplexing,” IEEE Access 6 (2018) 58587).
Although this technique successfully combines both plug and play with MDI-QKD, which simplifies the device structure for both Alice and Bob, it still requires the unbalanced interferometer at Charlie which requires a fiber loop and some degree of temperature control.
Another MDI-QKD system design that is also “plug-and-play” has been described in D. Stucki et al., “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys. 13 (2011) 123001 and the system block diagram is shown in FIG. 1A4. This system design is similar to, but an improvement upon, the design in Ref [Error! Bookmark not defined.].
This system again relies on an attenuated laser with decoy states and a Bell state measurement. In this case, however, the light source is located with the detectors at Charlie's node. This is a significant improvement for chip-based QKD. Now the PICs at Alice's and Bob's nodes do not need to include any of the expensive components that are also very difficult to integrate into a chip.
A significant difference with this system is that it makes use of time-bin/phase encoding rather than polarization state encoding. This makes the entire network system relatively immune from the birefringence effects of optical fiber, another significant advantage. This system operates in the following manner. Charlie generates a vertically-polarized coherent CW beam from a laser diode that is evenly split by a NPBS. One half of the beam is for Alice and other for Bob. Intensity modulators turn these beams into pulses. Not shown in the diagram is a means for ensuring randomness in the phases of each pulse for Alice and Bob. This is important for guarding against the unambiguous state discrimination attack (C. H. Park et al., “Practical plug-and-play measurement-device-independent quantum key distribution with polarization division multiplexing,” IEEE Access 6 (2018) 58587; H-K. Lo and J. Preskill, “Security of quantum key distribution using weak coherent states with nonrandom phases,” Qu. Infor. Comp. 7 (2007) 431-458). Each pulse for Alice is paired with a pulse for Bob with a fixed relative time shift between them so that when the paired photons from Alice and Bob eventually return to Charlie, they arrive at his PBS at the same time. A half waveplate (HWP) rotates the polarization state of Bob's beam by 90° to horizontal. The two beams are then recombined by a PBS. Alice's beam is now reflected by the PBS and remains vertically polarized. Bob's beam is transmitted by the PBS and remains horizontally polarized.
Both beams are split evenly by a NPBS and sent to unbalanced arms of a Michelson interferometer. The beams are reflected by Faraday mirrors so that their polarization is rotated by 90°. When they reenter the PBS, they are sent to the opposite port. Alice's beam, which was vertically polarized, is now horizontally polarized. Bob's beam has also been rotated in polarization. In addition, both Alice's and Bob's pulses have been split into two pulses of equal intensity by the unbalanced interferometer.
The next PBS then transmits Alice's pulses to the fiber that carries the pulses to her node. Bob's pulses get reflected by the PBS and sent towards his node. A HWP ensures that Bob's pulses are rotated back to horizontal polarization and transmitted by the next PBS into the fiber, while Alice's pulses are already properly horizontally polarized to be transmitted through the PBS and coupled into the fiber. When both sets of pulses leave Charlie's node, they are both horizontally polarized.
Alice's and Bob's devices are identical. The incident beam, which still consists of a large number of photons, is first attenuated and then split by a PBS. It should be noted that after transmission through the birefringent fiber, the polarization state of the light entering the PBS in Alice's or Bob's setups will generally be in some arbitrary polarization state. It will not in general be split evenly by the PBS, but different amplitudes of light will be split into the two optical paths. One path includes an intensity modulator that is designed to block one of the two pulses, randomly. By splitting the light with the PBS, it only passes one-way through the intensity modulator which may make the intensity control more precise, though in a related paper the two PBS's were not employed and the light just made a double-pass through the intensity modulator (H. Ko, B-S. Choi, J-S. Choe and C. J. Youn, “Advanced unambiguous state discrimination attack and countermeasure strategy in a practical B92 QKD system,” Qu. Infor. Proc. 17 (2018) 17). The light also passes through a phase modulator that adds an extra it-phase shift at random to the pulses. These are the two orthogonal bases for this system. The light is reflected by another Faraday mirror, thereby rotating its polarization by 90°. The part of the pulse that passed through the intensity modulator on the way in, now bypasses it on the way out, and vice-versa. A variable attenuator ensures that only a fraction of a photon in each pulse is passed back to Charlie. Because of the Faraday rotator, when the photons return to Charlie, their polarization is again linear and rotated by 90° to vertical in spite of any birefringence in the fiber thanks to the effect of the Faraday rotators. Therefore, the photons returning to Charlie from Alice and Bob are reflected by the first PBS they encounter and then arrive at a second BS simultaneously in the same polarization state for a Bell state measurement as described in the previous section.
A valid BSM occurs when Charlie measures a photon on opposite detectors in different time bins. If Alice and Bob select the time-bin basis, so that their photons arrive at Charlie's BS in either the first time-bin or the second, then when they choose opposite time-bins, there is a 50% chance that a photon from Alice or Bob will strike either detector—they are random and uncorrelated. If Alice and Bob, however, select the same time-bin, then two identical photons arrive at the NPBS at the same time. This is analogous to the HOM interferometer (Y. Choi, O. Kwon, M. Woo, K. Oh, S-W. Han, Y-S. Kim and S. Moon, “Plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 93 (2016) 032319) and both photons strike one or the other detector—there is no coincidence.
If Alice and Bob both choose the phase shift basis, then a coincidence on opposite detectors will occur when one of them has added a relative phase shift of π between the two time-bins of their entangled photon and the other has chosen no relative phase shift. (Alice and Bob could also include a ±π/2 basis. (C. K. Hong, Z. Y. Ou and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59 (1987) 2044) A table illustrating the detection criteria for the different bases is shown below.
When Charlie announces all the coincidences on opposite detectors that he measured, and Alice and Bob sift that list to determine which coincidences occurred when they both chose the same basis, then Alice and Bob, knowing the time-bin or phase shift that they themselves selected, will immediately know the state that the other selected as well and they can generate their secret key. When multiple photons arrive from either Alice or Bob in the phase shift basis, there can be accidental coincidences and a 50% error rate (Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian and H-K. Lo, “Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 112 (2014) 190503.)
In order for interference to take place, it is critical that the photons be indistinguishable in wavelength, polarization, and timing. The wavelength criterion is automatically fulfilled by using the same laser for photon generation for Alice and Bob. Polarization is also automatically fulfilled by the optics including the Faraday mirrors that correct for fiber birefringence. Therefore, the challenge in this QKD system is ensuring that the photons from Alice and Bob arrive at the same time at Charlie's NPBS. However, the timing error just needs to be small compared to the pulse length. In particular, the length of the pulses emitted by Charlie to Alice and Bob should be at least ten times longer than the inverse frequency linewidth of the laser and the electronic timing jitter in the pulse emission (Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian and H-K. Lo, “Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 112 (2014) 190503). Using longer pulses than this simply reduces the key rate. A typical pulse length is ˜2 ns. The wavefunction for a single photon defines the uncertainty in the photon wavelength. A photon wavefunction that is longer in time can have a much lower uncertainty in its frequency and vice versa. By making the pulse width ten times longer than the inverse laser linewidth, the actual linewidth of the emitted photon is then determined by the laser rather than by the pulse shaper. A longer the pulse provides a narrower the band of frequencies, but never smaller than the inherent linewidth of the laser.
It should also be pointed out that because two detectors are used, the efficiency of detecting both photons is proportional to the square of the single photon detector efficiency. Therefore, there is a premium on high efficiency SPD's. (Note that efficiency is the probability that a photon which strikes the detector generates a pulse. Probability of detection, on the other hand, includes the effects of all the intervening optics.)
The Charlie nodes contain the light source and detectors and may be located at either first nodes or second nodes in the network diagram in
It is also possible that a technician connected to the network at one edge node may need to communicate securely with a sensor or control at a different edge node. If the Charlie nodes are located at the smaller circles, then any two edge devices may be used to generate secure QKD keys. For example, if e2 needs to communicate with e11, the TSN scheduler sets up a fiber channel that connects either the M1 or M3 Charlie node to both edge nodes. In either case, the N1 and N2 nodes would simply be optical routers for the quantum channel (Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian and H-K. Lo, “Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 112 (2014) 190503; J. Li and C. Yang, “The design of a quantum Benes switch,” 2007 IEEE Conf. Electr. Dev. Sol.-State Circuits, Tainan, (2007) 539-544, doi: 10.1109/EDSSC.2007.4450181. They would not be involved in any QKD measurements directly.
Is it possible to locate the Charlie nodes only at the many fewer larger circle N nodes instead of the smaller M nodes in order to save the expense of light sources and single photon detectors as well as the amount of periodic maintenance costs? In other words, is it possible to make the M nodes just simple routers that connect desired edge devices to the N nodes? With only a single quantum fiber channel between the samller M nodes and the larger N Charlie nodes, there could be problems generating secure keys between some nodes. For example, if edge node e2 needs to communicate securely with edge node e4 that is connected to the same smaller node M1, and Charlie is located at the larger N1 node, then the N1 node needs to send photon pulses through a single quantum fiber channel between N1 and M1 to both edge nodes. We could send two separate pulse streams for Alice and Bob between the N node, Charlie, and the M node, Douglas, by ensuring that the pulse streams are orthogonally polarized, but after traveling through fiber between N1 and M1 the photons are in an undetermined, generally elliptical, polarization state due to the fiber birefringence. There is no simple way using a PBS, for example, to then separate the pulse streams for Alice and Bob. Wavelength division multiplexing (WDM) is also often used to send information to multiple end points over a single fiber channel. In this case, however, the photons sent to Alice and Bob must have the same wavelength in order to interfere at Charlie, so WDM is not an option. However, there are several potential solutions to this problem.
1) The fiber birefringence between the N node and the M node can be constantly measured, for example, by measuring the birefringence at two neighboring wavelengths on either side of the QKD channel and interpolating. As shown in
2) A straightforward approach for placing all detectors at Charlie's N node is to use polarization maintaining fiber between all M and N nodes for the quantum channel as shown in
Most of the components for the M nodes could in principle be integrated onto a PIC chip, though it would be much easier with current technology to build the M nodes from discrete components. The most difficult components to integrate into the M nodes are the laser diode and the optical delay line. However, these components have been successfully integrated (L. Lu, S. Zhao, L. Zhou, D. Li, Z. Li, M. Wang, X. Li and J. Chen, “16×16 non-blocking silicon optical switch based on electro-optic Mach-Zehnder interferometers,” Opt. Exp. 24 (2016) 9295-9307). A delay line of 7 m (35 ns) was demonstrated in an integrated chip with a total loss of 0.56 dB and potential for loss reduction down to 0.01 dB/m (P. Sibson, et al., “Chip-based quantum key distribution,” Nat. Commun. 8 (2017) 13984). Another issue in fabricating the M node into a PIC may be the optical losses occurring at the light couplers for getting light off and on the chip. Although PM fiber is required between N and M nodes in this case, the most expensive components, the single photon detectors, are located now at the highest level of the network with the fewest nodes.
3) Another way to multiplex the light pulses to Alice and Bob over a single fiber between Charlie and Douglas is through timing as shown in
This problem can be overcome by generating the time delay between the two pulse streams at Charlie's node. Because the physical distance between Douglas and either Alice or Bob is most likely very similar according to the star network design, this approach may make more sense anyway. As shown in
The light polarization for the beams to Alice and Bob as they move through this system are given in Table 5. The probability of photon detection at Charlie's single photon detectors depends on the basis and specific state chosen by Alice and Bob is shown in Table 4 for single photons from Alice and Bob and ideal optics. A detailed discussion of the detection probability for multi-photon emission and nonideal detectors is given in the appendix pursuant to calculating the practical key generation rate.
This table exhibits how the polarization state of the two photon pulses for Alice and Bob vary throughout the entire optical system including Charlie. However, because of the birefringence in the fiber channel, the polarization state is only well-defined at Charlie.
As an example of the connection between the hardware and the network configuration, the hardware components in
Returning to alternate approaches to enable intermediate switching and routing between edge devices and Charlie's node for which there is only one optical fiber path:
4) The simplest solution is to require two or more quantum fiber pathways between M1 and N1. This redundant pathway may already be incorporated in a QKD network for reliability. Then the TSN scheduler ensures that the photon pulses sent and received to/from Alice and Bob follow the different pathways. As shown in
Four different options for locating the expensive equipment, or at least the detectors, at the Charlie nodes have been discussed. Of these options, it would seem that the arrangement in
Putting this all together with the TSN scheduler, the TS-QKD network configuration could look something like that in
Returning to a viable P&P MDI-QKD design such as that shown in
Before discussing an invention for synchronizing events enabling MDI-QKD, it should be recognized that there are a plurality of quantum network algorithms and protocols that require the ability to configure the network in preparation for simultaneous events and to determine whether those events indeed happened simultaneously. Examples include but are not limited to, Superdense Coding, various QKD protocols, and in general, numerous network entanglement-based protocols.
The quantum network can be conceptually divided into a data plane, which is the conceptual model of paths and supporting equipment over which the main communication traffic flows, and the control plane, which is the conceptual model of paths and equipment over which the network is configured and controlled. The data plane comprises single-photon and entangled-photon transport and manipulation. The control plane comprises classical, remote configuration and operation of the data plane.
A network configurator (NC), or alternatively, centralized network configurator (CNC), manages and controls the entire network. The CNC has complete information about network topology. Topology information can be manually entered or every device on the network (end-systems and switches) reports information about its immediately adjacent connections (neighbors) enabling the entire interconnectivity of the network to be discovered by the CNC. This includes both classical (e.g., Ethernet or wireless) devices and connections as well as quantum optical devices and connections. This is defined for classical systems for the IEEE802.1 standard (G-Z. Tang, S-H. Sun, F. Xu, H. Chen, C-Y. Li and L-M. Liang, “Experimental asymmetric plug-and-play measurement-device-independent quantum key distribution,” Phys. Rev. A 94 (2016) 032326). We assume that the quantum channels will be likewise advertised via this classical protocol. That is, every QKD component will also be connected to a classical network, which will also report it's optical and quantum connections to nearest neighbors. The CNC uses QKD-generated keys to authenticate and encrypt communication with all network devices.
For the classical control plane, the maximum size of every message is known, a priori, by the CNC, where message size is used to compute message transmission time. For the quantum data plane, a single-photon message size is simply the duration of time between the request for transmission of a single photon and the time the photon is actually emitted by the device. Note that for a classical system, this can be known with a high degree of determinism, but for a quantum system, a Poisson mean value may be the most that can be determined.
The propagation delay along every link is also known a priori, inferred either via cable length or via a variety of means that involve echoing a small message from adjacent neighbors. We also assume the CNC can query optical components within the network for the single-photon propagation delay of quantum fiber channels.
A separate time synchronization protocol, for example, one of the many profiles (variants) of Precision Time Protocol (PTP), known as gPTP (https://github.com/YangModels/yang/blob/master/standard/ieee/draft/802.1/ABcu/ieee8 02-dot1ab-lldp.yang), maintains clock synchronization throughout the entire network. This is accomplished by ensuring network interfaces support hardware timestamping, enabling accurate and precise timestamps that are placed in short messages exchanged in order to measure link delay. Timestamping is done within the hardware as close to the “wire”, e.g. the physical link, as possible to ensure no jitter or delay occurs from anything other than propagation time over the link. Typically, messages are sent and returned with appropriate timestamps allowing the device initiating the propagation delay measurement to divide by two assuming the link is symmetric. Propagation delay measurements are performed periodically to ensure up-to-date results.
Once link propagation delays are known, synchronization messages are exchanged that contain the current clock tick rate. A clock is identified as a grandmaster clock and all other clocks adjust their tick rate ratio such that their time matches the grandmaster's notion of time. Since clocks are clearly defined relative to one another in a master-slave relationship forming a spanning tree, clock rates are adjusted relative to one another such they all match the grandmaster clock. Put another way, grandmaster time can be reconstructed by every clock in the network. There is always error, however small, typically measured in root mean square (RMS) nanoseconds. Error is dependent upon the stability of the clocks, how often the synchronization messages are sent, and in a large network, on placement of the grandmaster within the network topology relative to the other clocks. All PTP message exchanges are authenticated and encrypted using QKD-generated keys.
At this point, the network is time synchronized, and the CNC knows all message sizes, the network topology, and all link propagation delays. The CNC also knows the source and destination of all messages in the network, including all classical control messages and all quantum data plane messages. If the CNC is provided with the maximum-tolerated latencies for each pair of end-systems that need to communicate, the CNC can determine a single-photon path and schedule when each device along the path should transmit the photon. The CNC must compute initial transmission (photon emission) and periodic opening and closing times of gates (switches) for each device along a network path such that messages are sent and received at precise, periodic intervals forming a connected path while simultaneously avoiding collision within the network. Collision occurs when transmitting more than one message at the same time (such that the photons, in this case, would overlap) over the same link. However, as mentioned, there are quantum networking algorithms where the goal is to create a perfect collision, namely a simultaneous event where two messages (single photons) arrive at the same location at the same time. And the goal is to accomplish this simultaneous event periodically. Although this is something a network scheduler typically seeks to avoid, it is an interesting task to add to the scheduler's capabilities. This is accomplished using TSN via the following steps: (1) identify specific Alice and Bob devices and label them as TSN Talkers within the CNC scheduler (2) identify the Charlie device and label it as a TSN Listener in the CNC scheduler (3) set the maximum TSN latency for the Talker-Listener flows to be the longer of the Alice-Charlie and Bob-Charlie optical propagation delay times (4) compute the TSN schedule, which results in a periodic cycle time with offsets within the cycle for the Alice and Bob nodes to transmit. It should be noted in step (3) that the maximum flow latency must be computed such that messages arrive at precisely the same time and rather than any time less than the maximum. This requires a change to the typical TSN scheduler solver.
In a classical setting, the CNC attempts to meet or exceed the required minimum latencies for each deterministic flow. This can be tightened to provide exact latencies. Also note, that in a strictly classical Ethernet setting, the CNC is controlling the flow of a classical data plane. However, the control plane can remain classical, while the data plane is quantum. The CNC can send configuration information to configure known, deterministic paths through the quantum data plane at precisely periodic time intervals. Typically, this would be done via a YANG module that exposes network configuration and control information about a device in a well-described manner. The CNC would have to either manually be provided with the required quantum channel paths or be able to query and learn about the quantum network via something like NETCONG/YANG or Link Layer Discovery Protocol (LLDP) and infer when specific quantum channel paths are required. For example, if the CNC were provided with the fact that certain network devices identified themselves as Alice, Bob, or Charlie and the duration of time connections are required among Alice, Bob, and Charlie, then the CNC computes and configures such connectivity for the entire network. The CNC makes the decision as to which Alice, Bob, and Charlie combinations are optimal for the network, depending upon their locations, capabilities, and QKD key consumption requirements within the network.
Since the network is time synchronized, the CNC can also provide to Alice and Bob meaningful information about whether, and precisely when, a coincidence event happened at Charlie and serve to provide additional support and verification of events necessary for MDI-QKD.
There exist numerous scheduling algorithms that can be used by the CNC.
If Alice and Bob are edge devices that are part of a TSN network, then the “node” e.g. Alice, Bob, or Charlie, MUST have a network clock. Each network output port has its own clock in TSN to control the gates. All clocks on the device are synced to network time. The QKD chip can use this clock for timing. Alice and Bob use timing, for example, to modulate the pulses from Charlie, determining which pulses to shutter or pass, which pulses to phase shift or not phase shift, and which pulses are decoy states that have a different average number of photons.
Another interesting difference between classical use of the CNC and this invention is that classically, the CNC computes a single cycle time with offsets indicating when each network event occurs, and this cycle time and these offsets remain constant over many cycles. In this invention, propagation delays may need to be updated more often due to sensitivity of fiber length on propagation delay. It is recognized that re-computation should only be done when propagation delay changes are significant enough to warrant a re-computation. This could be determined, for example, by a noticeable drop in the key production rate. It should also be noted that the CNC is now controlling things like coincidence detection windows and photon detector gating as well as network switches and classical Qbv gate control.
The CNC can indicate when Charlie is to send his initial calibration pulse to both Alice and Bob and configure the network switches such that the pulse travels to Alice and Bob and back to Charlie so that Charlie can then determine the correct time delay, report that back to the CNC, and the CNC can tell Charlie again when to send his QKD pulse sequence to Alice and when to send it to Bob, while ensuring that the appropriate network path/switches are selected.
Alternatively, if Alice's, Bob's, and Charlie's clocks are perfectly synchronized, then Alice and Bob only need to timestamp when they received Charlie's pulse, and report that to the CNC, and Charlie only needs to report to the CNC when he sent the pulse. Then the CNC can tell Charlie when to send his QKD pulses to Alice and Bob and also when to expect the return coincidence. The latter is important because Charlie may need to gate his detectors to just look for the return photon coincidences from Alice and Bob within a narrow time window to eliminate dark count noise from his detectors.
Since Charlie is assumed to be untrusted, careful consideration should be made regarding what capabilities are placed on Charlie. For example, Charlie should not be a grandmaster clock. Finally, there is a chicken-and-egg problem: Charlie is participating in network time synchronization and scheduling, assuming QKD-protected message exchanges, before QKD keys are being generated. One could address this by simply not including Charlie in the time synchronization and scheduling processes, only Alice and Bob (trusted nodes) need to participate in time synchronization and scheduling. However, if Charlie were to attempt to report misleading values, it will fail to create simultaneous events leading to detectable error.
As shown in
Charlie notes the time difference between his detection of the two pulses and communicates this to the TSN scheduler if necessary. The TSN scheduler then selects the same route and opens the channel for the QKD key distribution to Alice and Bob at the appropriate instants (which may be different depending on the time delay required). Charlie now knows the delay he must use between the photon he sends to Alice and the one he sends to Bob so that the reflected photons arrive at his NPBS at the same instant. When triggered by the TSN scheduler, he then sends his sequence of pulses to both Alice and Bob with the appropriate delay. The TSN scheduler can set up this time calibration routine as frequently as required so that the slow drifts in the speed of light over fiber that are occurring constantly do not affect the quantum key distribution.
A basic photonic integrated circuit chip design that operates at telecom wavelengths (typically 1550 nm) is shown in
The red arrows indicate the light path for a vertically polarized photon from the fiber which enters the chip with TM polarization, is rotated to TE polarization, and follows a clockwise path around the chip. It first encounters a 90:10 tap which sends some of the incident light to an analog (usually germanium) photodetector to sense for bright light attacks. The rest of the light continues around the loop through a variable optical attenuator that reduces the light level so that during key generation it is unlikely to emit more than one photon, an intensity modulator for adjusting the average number of photons between the key level and the decoy level(s), and a phase shifter to randomly modulate the photon phase by either 0 or π. The photon returns to the polarizing beamsplitter where it is out-coupled into the fiber as horizontally polarized light.
If the incident photon is horizontally polarized, it enters the waveguide as TE polarization, follows a counter-clockwise optical path, going first to a second 90:10 tap and photodetector to sense for a bright light attack, and then through the remaining components in reverse order (order does not matter). The photon is then coupled back into the waveguide through a polarization rotator which converts it to TM polarization before reentering the fiber with vertical polarization. (TE & TM are orthogonal polarization states in waveguides, just like H and V are for free space. There is no interference between these two waveguide modes in linear media.) A bit stream from Charlie is passing through A & B sequentially. Because the waveguide path length is so short on the chip, there will only be one pulse in the chip at any time. Hence, Alice and Bob must be able to switch their modulators fast enough to operate on the individual pulses.
Generally, it is desirable to maintain TE polarization in the PIC, because the electric field for the TM waveguide mode extends further into the cladding and can interact with the Si substrate. Therefore, the TM mode is typically attenuated much more than the TE mode. However, as Alice's and Bob's nodes both contain attenuators anyway to reduce the reflected photon count to less than one, it is not critical that the chip be designed for TE mode. On the other hand, most of the components in the process development kit (PDK) for a typical CMOS PIC foundry are designed and optimized for TE mode. Furthermore, birefringence in the fiber will be constantly changing the polarization state at the input coupler to the PIC. However, it is not desirable to have the amount of photon attenuation change over time as the amount of input light in each polarization state changes. Therefore, by converting the input light regardless of polarization to TE mode, the light attenuation on the chip should remain relatively constant.
More fundamentally, the photons reaching Alice and Bob are in an arbitrary polarization state due to the fiber birefringence. Therefore, the PBS will split the beam, some light going left and some going right. Both parts of the beam are phase shifted and attenuated (since the phase shifters and attenuators don't care which way the light passes through them) and then are recombined with the opposite polarization state before being returned to Bob. Whichever path the incoming photon decides to follow, its arbitrary polarization state gets rotated by 90 degrees and is then returned to Charlie. The birefringence in the fiber then “undoes” the randomness it generated on the way out so that by the time the photon reaches Charlie, it is returned to linear polarization but rotated by degrees.
A timing diagram that shows how the chip modulates the intensities and phases of the return pulses is shown in
Because of the polarizing beamsplitter/polarization rotator (PBS/PR) combination at the entrance of the chip, the returning photon has had its x/y polarization components interchanged as occurs in a Faraday mirror so after the photon returns to Charlie through the fiber cable, the effect of birefringence is eliminated. This is a critical feature of plug-and-play systems that enables the birefringence in the fiber to be neglected. When the photon reaches Charlie's apparatus as shown in
It is interesting to also calculate the key generation rate for the plug-and-play MDI-QKD technique described in the previous section. The derivation of the calculation technique is quite tedious as shown in the appendix. Key generation rates using InGaAs single photon detectors are relatively low compared to higher efficiency SNSPDs due to their much higher background dark count rates and lower detection efficiencies. We can compare the key generation rates as a function of distance for these different detectors. Following the procedure in Z. Yong et al., “U-shaped PN junctions for efficient silicon Mach-Zehnder and microring modulators in the O-band,” Opt. Exp. 25 (2017) 8425, we calculate the key rate for up to three photons (a three-photon Fock state) arriving at Charlie's BS from both Alice and Bob. More fundamentally, Charlie emits billions of photons in his pulses, but Alice and Bob attenuate them to on average ˜0.5 photons/pulse. However, since the actual number of photons remaining in a pulse follows a Poisson distribution, sometimes there will be more than one photon in a pulse and sometimes there will be no photons in a pulse. Even if there are more, by the time they travel back to Charlie most pulses will only have zero or one photon left. Very, very few pulses have more than one photon, so we can safely ignore four or more photons per pulse when we calculate probabilities.
With suitable attenuation of the reflected photons it is very unlikely that more photons than this will arrive at Charlie's BS. The standard key generation rate equation (i.e., the rate per pulse for which signal photons in the |Ψ−singlet Bell state detected by Charlie and sifted to have been sent in the same basis by Alice and Bob) is (P. Chan, J. A. Slater, I. Lucio-Martinez, A. Rubenok, and W. Tittel, “Modeling a measurement-device-independent quantum key distribution system,” Opt. Exp. 22 (2014) 12716-12736)
R≥w[Q
11
z
−Q
11
z
H
2(e11x)−QμμzfeH2(eμμz)] (1)
where w is a factor that accounts for the protocol efficiency and number of decoy states, Q11z is the gain in the Z (time-bin) basis, H2 is the binary Shannon entropy,
H
2(x)=−x Log2(x)−(1−x)Log2(1−x), (2)
e11x is the error rate in the X (phase shift) basis for single photons emitted by Alice and Bob, Qμμz is the gain and eμμz is the error rate in the Z (time-bin) basis when Alice and Bob emit on average m photons per pulse. For the calculations we assume a HOM visibility of 0.99 to account for optical misalignment, μ=0.4 (the average photon level in the signal state), an error correction overhead fc=1.16, and w= 1/18 for pulses evenly divided between a signal level and two decoy levels. The wavelength/detector parameters are listed in Table 7. For the calculation we assume Alice and Bob have detectors with the same characteristics and are located the same distance from Charlie. Calculated key generation rates are shown in
At all distances the SNSPDs provide the highest key generation rates as expected. If Charlie emits pulses at 50 MHz, for instance, then key bits can be generated at tens of thousands per second for short distances. With InGaAs SPADs the key generation rate drops to just shy of 1 kbit/s, which is still quite reasonable for this proposed power grid application. With the SNSPDs, key rates of ˜50 bits/s can still be generated up to ˜70 km distances between Alice (or Bob) and Charlie.
A basic QKD chip design is shown in
There are a variety of other approaches to RNG including amplified spontaneous noise (K. Ugajin et al., “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Exp. 25 (2017) 6511-6523) and quantum noise (C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Exp. 18 (2010) 23584-23590). Obviously, incorporating the RNG on the same chip as the QKD device reduces part count, cost, and enhances security, but the thermal noise approach to RNG is probably suitable and simpler for the low key rates required by most edge devices.
The plug-and-play concept eliminates the light source from the end nodes, Alice and Bob. Yet, Alice and Bob still need to communicate with each other in some manner after generating the key. If we would like to keep lasers for classical communication off of the PIC chips to simplify chip integration, then either there is a laser source off-chip at Alice and Bob that can be coupled through the chip (with attendant losses) for modulation, or the laser can be located at Charlie. Charlie could generate a CW light source either at the same wavelength as the QKD key generation system, or by using wavelength division multiplexing use a different telecom band wavelength. He sends the classical laser light to either Alice or Bob or both, who then use their attenuators to modulate the beam and return it to Charlie. A circulator then routes the encrypted return beam to the other party for communication as shown in
Charlie could also split-off part of the return beams from Alice and Charlie to monitor for transmission directed to him, i.e., if either Alice or Bob wants to initiate key generation or communication with another party. Of course, this wastes bandwidth to have Charlie continuously sending a CW laser beam to each edge device which might need to initiate communication. Charlie could also intermittently send a beam to every edge device to see if that device wanted to communicate. If a new edge device is added to the network, then there must be a means to alert Charlie to its presence.
The primary disadvantage of this approach is that neither Alice nor Bob can initiate the communication unless Charlie is continuously sending a CW beam to each of them. In order to eliminate this problem, Alice and Bob will need to have a separate communication source which could be a laser to communicate over the fiber network, or perhaps WiFi to connect to a wireless network. If Alice and Bob incorporate laser sources on their PIC chip, then they could use WDM to communicate with other nodes on a wavelength other than that used for QKD. In that manner, they could potentially be generating a key simultaneously as they are transmitting information. An example is shown in
Finally, it should also be mentioned that for short distance QKD communication it may be possible to use shorter wavelength photons. The attenuation with distance through optical fiber is currently quite large for visible light wavelengths precluding long distance communication. However, future development of hollow core fiber looks promising to achieve low loss fiber at essentially any desired wavelength. At visible light wavelengths, Si avalanche photodetectors have high detection efficiency and very low dark counts without the need for cryogenics. In addition, they are much less expensive than superconducting or InGaAs detectors. Therefore, a QKD chip built for shorter wavelengths could have the benefit of reducing hardware costs for Charlie. The main problem is that Si waveguides on PICs are opaque to visible light. SiN waveguides on PICs, on the other hand, are quite transparent. If a PIC QKD chip is fabricated for visible light using SiN waveguides, then the only remaining difficulty is modulating intensity and phase shift of the light pulses. This cannot be done with SiN components, but it is possible using hybrid chips with III-V semiconductors to modulate visible light wavelengths. Steady progress is being made to integrate III-V components with Si chips because it also enables the presence of other active components light laser diodes. Therefore, it is definitely possible that QKD could be accomplished via hybrid PICs and visible light over short distances with current solid core fiber (˜1 km) and over much longer distances in the future with successful development of low loss hollow core fiber.
In this disclosure we have discussed various QKD techniques and protocols based on polarization or time-binning and phase shifting. In particular, we have discussed and analyzed in detail a new QKD technique that can be completely implemented on a PIC chip for all Alice and Bob edge devices. One big advantage of this approach is that it is based on MDI-QKD, so it is inherently secure from any of the most likely side channel attacks involving the imperfections in single photon detectors. There is still a required Charlie node on the network that involves expensive and large equipment, not implementable on a PIC chip, but this node can be untrusted and by implementing a network design as described in this report, the number of Charlie nodes can be greatly reduced to perhaps one node per central monitoring station. In principle, this approach, like entanglement-based techniques, also extends the QKD communication distance over that achieved by prepare-and-measure QKD techniques (H-K. Lo, M. Curty and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108 (2012) 130503). We have also argued that a hybrid approach will be necessary for a QKD-protected power grid network. Nodes connected over long distances (>50-100 km) through fiber will most likely require more expensive equipment like cryogenically-cooled SNSPDs which will be larger and have much higher power and maintenance requirements. Shorter distance communication between a station and edge devices can be accomplished with InGaAs SPADs at the Charlie nodes with much lower cost and lower power requirements than SNSPDs. The edge devices, Alice and Bob nodes, can make use of low cost, robust integrated QKD photonic chips.
Various other QKD techniques have also been critically examined. The “reference frame-independent QKD” (rfiQKD) system (http://www.aimphotonics.com/; A Laing, V. Scarani, J. G. Rarity, and J. L. O'Brien, “Reference-frame-independent quantum key distribution,” Phys. Rev. A 82 (2010) 012304) design does not require any light sources or detectors at Bob's node and can in principle be fabricated with current technology. Alice's system is more complex and expensive, but in principle for shorter distances Alice could use much less expensive near IR light source and single photon detectors. By using an attenuated laser for the light source, the “on-demand” issue is relieved. Another advantage is that it follows the BB84 QKD protocol with well-established security proofs using the decoy state for attenuated light sources. The primary disadvantage is that Alice's node cannot be implemented in a PIC chip. Furthermore, Alice and Bob must be connected through two polarization maintaining fibers. Therefore, it is unlikely that an existing fiber network could be employed.
Alternatively, CV-QKD has been developed as a protocol that does not require single photon emitters or single photon detectors. This makes it more amenable to “on-demand” key generation than the entangled photon protocols. More importantly, perhaps, is the fact that homodyne/heterodyne detection systems with germanium detectors have already been demonstrated on-chip. Although security proofs for this protocol are not as complete as for most of the single photon/entangled photon protocols, it may still be an attractive option due to its much lower cost and power requirements for the total system (Alice+Bob). CV-QKD typically requires a high degree of polarization control as well as amplitude and phase modulation. The primary technology gap for this technique is polarization control, which is currently difficult or impossible to adequately integrate on-chip, though the other components for this QKD system can be easily fabricated. Homodyne detection enables lower cost detectors so that communication can be accomplished over longer distances in the telecom band without special cooling requirements. This approach could be used for node-to-node communication if the security proofs are acceptable. Current key generation rates for this design must be greatly improved, however.
Ultimately, an integrated Si photonic chip offers many advantages over larger instrumentation besides just cost and power consumption. Long term stability is greatly improved as alignment and dust are not issues. All components can be directly coupled together on-chip with much higher efficiencies, and operating speeds can be much higher (P. Zhang, et al., “Reference-frame-independent quantum-key-distribution server with a telecom tether for an on-chip client,” Phys. Rev. Lett. 112 (2014) 130501). Integrating the laser source and single photon detectors on-chip cost effectively are big challenges, in addition to polarization control if needed. QKD chips that require components like lasers, SPDs, fiber delay lines, and polarization control may need to use them as off-chip components, and this will eliminate most, if not all, of the cost and size advantages of PIC chips.
As discussed, several technology gaps have been identified with the currently published QKD techniques applied to PIC chips. An on-chip light source is a primary concern. For CV-QKD this would probably require integrating a separate diode laser onto the chip with efficient light coupling into a waveguide. This is currently a research topic and goal for many photonic chip manufacturers and will likely be solved satisfactorily on its own. On-chip photon pair generation has been demonstrated using nonlinear waveguides. Polarization entanglement of the photon pairs is required for many DV-QKD techniques and has been reported by one group, but careful design of the waveguide for TE/TM mode propagation is required. An on-chip, on-demand entangled photon source has yet to be designed and fabricated, which is a large technology gap for several techniques. General-purpose polarization control as well as specialty components like isolators, circulators, and Faraday mirrors are currently difficult or impossible to implement on-chip. If a diode laser is integrated on-chip, for example, then isolators will likely be required. Many of the implemented components require strict temperature control, and the desired temperatures may be incompatible on the same chip. Long time delays now accomplished through tens of meters of fiber cannot be implemented on-chip, another technology gap. While one solution may be to couple light from the chip into an off-board fiber or other component, the optical losses for in- and out-coupling to fiber may be prohibitive. Therefore, the new technique described in this report is a significant advancement in the state-of-the-art and may make QKD cost effective and implementable through industrial control systems, including the power grid.
As will be appreciated by those of skill in the art, the systems and methods described herein may be used in 5G communications systems. For example, quantum key distribution and measurement-device-independent quantum key distribution may be used to protect fiber portions of a 5G network, using the embodiments described herein.
A/D: anti-diagonal/diagonal (basis)
AM: amplitude modulation
AMZI: asymmetric Mach-Zehnder interferometer
AO: acousto-optic
APD: avalanche photodiode
BB84: Bennett and Brassard QKD protocol from 1984
CV: continuous variable
CW: continuous wave
DFB: distributed fiber Bragg (grating)
DV: discrete variable
EO: electro-optic
H/V: horizontal/vertical (basis)
LN: lithium niobate
LO: local oscillator
MZI: Mach-Zehnder interferometer
MZM: Mach-Zehnder modulator
PBS: polarizing beamsplitter
PC: Pockels cell
PDK: process development kit
PM: polarization maintaining (fiber) or phase modulation
QD: quantum dot
QKD: quantum key distribution
R/L: right-/left-circular polarization (basis)
SFWM: spontaneous four-wave mixing
SM: single mode (fiber)
SNR: signal-to-noise ratio
SNSPD: superconducting nanowire single photon detector
SPAD: single photon avalanche detector
SPD: single photon detector
SPDC: spontaneous parametric down-conversion
TE: transverse electric
TM: transverse magnetic
TSN: time-sensitive network
TS-QKD: time-sensitive QKD
UCSB: University of California, Santa Barbara
VCO: voltage-controlled oscillator
WDM: wavelength division multiplexer
It is to be understood that the above description is intended to be illustrative, and not restrictive. For example, the above-described embodiments (and/or examples thereof) may be used in combination with each other. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the inventive subject matter without departing from its scope. While the dimensions and types of materials described herein are intended to define the parameters of the inventive subject matter, they are by no means limiting and are exemplary embodiments. Many other embodiments will be apparent to one of ordinary skill in the art upon reviewing the above description. The scope of the inventive subject matter should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. Further, the limitations of the following claims are not written in means-plus-function format and are not intended to be interpreted based on 35 U.S.C. § 112(f), unless and until such claim limitations expressly use the phrase “means for” followed by a statement of function void of further structure.
This written description uses examples to disclose several embodiments of the inventive subject matter and also to enable a person of ordinary skill in the art to practice the embodiments of the inventive subject matter, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the inventive subject matter is defined by the claims, and may include other examples that occur to those of ordinary skill in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.
The foregoing description of certain embodiments of the inventive subject matter will be better understood when read in conjunction with the appended drawings. To the extent that the figures illustrate diagrams of the functional blocks of various embodiments, the functional blocks are not necessarily indicative of the division between hardware circuitry. Thus, for example, one or more of the functional blocks (for example, processors or memories) may be implemented in a single piece of hardware (for example, a general-purpose signal processor, microcontroller, random access memory, hard disk, and the like). Similarly, the programs may be stand-alone programs, may be incorporated as subroutines in an operating system, may be functions in an installed software package, and the like. The various embodiments are not limited to the arrangements and instrumentality shown in the drawings.
As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural of said elements or steps, unless such exclusion is explicitly stated. Furthermore, references to “one embodiment” of the inventive subject matter are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Moreover, unless explicitly stated to the contrary, embodiments “comprising,” “including,” or “having” an element or a plurality of elements having a particular property may include additional such elements not having that property.
This application claims priority to U.S. Provisional Patent Application No. 63/083,484, filed on Sep. 25, 2020, which is hereby incorporated by reference in its entirety.
This invention was made with government support under contract DE-OE0000894 awarded by the United States Department of Energy. The government has certain rights in the invention.
Number | Date | Country | |
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63083484 | Sep 2020 | US |