Patent Application
20240125644
The section headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described in the present application in any way.
Systems that exchange information using single photons are useful for a wide variety of computing, communication, and measurement applications. One example of such systems are systems that use photon phase correlation to perform sensing and measurement. This includes quantum ghost imaging and various other optical imaging systems. For these systems, the sharing of classical state information, quantum state information, and various hybrids of these can be used to increase secrecy, accuracy, precision and speed of data taking as compared to classical systems. As such, methods and systems that support and improve state information transfer using single photons is useful in advancing the state-of-the art identification and measurement systems. Of particular interest currently are systems that exploit time correlation across sets of photons that number more than two.
The present teaching, in accordance with preferred and exemplary embodiments, together with further advantages thereof, is more particularly described in the following detailed description, taken in conjunction with the accompanying drawings. The skilled person in the art will understand that the drawings, described below, are for illustration purposes only. The drawings are not necessarily to scale; emphasis instead generally being placed upon illustrating principles of the teaching. The drawings are not intended to limit the scope of the Applicant's teaching in any way.
The present teaching will now be described in more detail with reference to exemplary embodiments thereof as shown in the accompanying drawings. While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. Those of ordinary skill in the art having access to the teaching herein will recognize additional implementations, modifications, and embodiments, as well as other fields of use, which are within the scope of the present disclosure as described herein.
Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the teaching. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment.
It should be understood that the individual steps of the methods of the present teachings can be performed in any order and/or simultaneously as long as the teaching remains operable. Furthermore, it should be understood that the apparatus and methods of the present teachings can include any number or all of the described embodiments as long as the teaching remains operable.
Quantum entanglement is a powerful resource that has numerous applications in a variety of processing, sensing and communications applications. One important and basic requirement for the efficient and effective use of quantum entanglement is the need to quickly and/or easily identify the entangled resources. For example, each photon in a pair of entangled photons can carry state information that is entangled such that the values of those states are the same when measured. As such, it is necessary to identify photons that are part of a pair of entangled photons, to know that a particular measured value is one of two shared correlated values. Generally, each photon in a set of entangled photons can carry state information that is entangled such that the values of those states are the same when measured. For optical measurement applications, the correlation of entangled photons, specifically in a phase dimension and/or a time dimension, can produce very precise time and/or position measurements. In addition, for optical measurement applications, the non-local correlation of entangled photons can be used to provide a point-to-point image correlation between optical detections at an object plane and an image plane. These applications require the timely and accurate identification of photons that are part of a set of entangled photons in order to know the measurements using the photons of the set are correlated.
Identifying photon sets that are entangled, and the corresponding measured state values that are correlated, is notably different from classical resource identification systems or methods. This is particularly true when classical systems and methods are used for optical measurement systems because these systems typically produce, process, and detect large numbers of photons. Some of the differences arise, at least in part, because the measurement of a photon collapses any associated quantum state or states in an irreversible way. Some of the differences arise, at least in part, because quantum resources can be quantized where their states take on only specific and/or singular values that are not characteristic of large numbers of photons and the associated analog opto-electronic detection of those photons. Some of the differences also arise because entangled resources carry perfectly correlated state information. Also, some of the differences arise because of various combinations of these qualities.
Another important difference between identifying classical data sets and identifying entangled photons and their associated correlated state values arises because many well-known, low cost, sources of entangled photons generate orders of magnitude more photons that are not entangled compared with photons that are entangled. Also for many practical systems, the photons that are not entangled must not be erroneously identified as entangled. This results in a kind of high background single photon noise condition. Quite different from classical situations, it is possible to find and process quantum information that is surrounded by very high single photon backgrounds. In contrast, classical optical detection and measurement systems reach a point where it is not possible to detect and process an optical image or other signal once the signal level falls sufficiently below a classical noise level. In contrast, the entangled photon identification method and system of the present teaching can operate when a number of legitimate entangled, correlated photons in a measurement window is multiple orders of magnitude less than a number of non-entangled background photons or background counts from other sources in that same measurement window. In fact, many engineering design “rules of thumb” that are commonly accepted and used for classical imaging and measuring systems are not usable or have limited use in similar quantum versions of those imaging and measuring systems. This can be true even if the classical apparatus and quantum apparatus share the same, or similar, physical structure.
The performance of entangled photon identification is also subject to lost photon events that can create error conditions. There is an expectation that a correlated state value at one location from measurement of one of the photons in the set has a correlated pair state value at a second location from measurement of another photon in the set, and this measured state value is not present, causing an error in the correlated data sets.
For purposes of the present teaching, we describe two different forms of quantum information: quantum information in a quantum form and quantum information in a classical form. Quantum information in a quantum form includes quantum information in a potential state. Some refer to a potential quantum state as “res potentia”, that is, offering possibilities. Examples of a potential state include a coherent state, a superposition state, and an entangled state. In some cases, a potential quantum state is a state that is unknown and/or not yet measured. We also use the term quantum information to include information in a classical form. This quantum information includes, for example information in a measured or collapsed state. This kind of quantum information is, for example, the outcome of a measurement of potential state that yields a particular state value (e.g., one of the possible superposition states). We also use the term quantum information in a classical form to include wavefunction information that can include a deterministic description that bounds and/or provides the evolution of a potential state of a quantum system. Although both the measured states and the wavefunction information are quantum information, they differ from the potential state information in that they are classical in nature. For one thing, they are actual or known. Also, they can be communicated over classical channels and used and/or processed by classical information systems, including classical memory, CPU, analog and/or digital processors, and a variety of classical sensing and measurement systems that may be analog and/or digital in nature, without any fundamental change to their properties.
It is important to emphasize that quantum information in a quantum form has certain quantum properties e.g., quantization, superposition, non-locality, correlation and combinations of these qualities. A quantum potential state description applies when the system is coherent or still in superposition. A notable quality of the potential state is that at least some of the quantum state information is not known. Once the carriers of quantum state information in a quantum form e.g., photons, atoms, ions, and superconducting junction currents, are measured to yield the quantum state information, the states of those carriers are collapsed, and therefore yield measured quantum state information is then in a classical form. This measured quantum state information is classical in nature, and can be further processed in a classical way, but yet it is intimately connected to the quantum nature of the potential state that was measured, which are reasons why it is referred to herein as quantum information. As examples, non-locality, and correlation properties are characteristic of quantum information in a classical form. These properties are not possible with purely classical information derived from classical systems.
In addition to the above description of the different forms of quantum and classical information, it is important to consider how the systems and applications use the quantum information. Some applications and systems that use quantum information use a portion of the quantum information they intake to directly process, store, measure, sense and/or communicate. It is convenient for the purposes of this disclosure to refer to this portion of the quantum information as the quantum data. Another portion of the quantum information the applications and systems receive is used to aide in the processing, measuring, sensing and/or communicating of the quantum data. It is convenient to refer to this portion of the quantum information as the quantum metadata.
The quantum data and quantum metadata terminology are analogous to the use of the term metadata in information technology as referring to information about the data, as opposed to the data itself. The portion of quantum information that is considered quantum data and the other portion of quantum information that is considered quantum metadata is more closely tied to the application or system that is using the quantum physical system. In contrast, whether quantum information is in a classical form or a quantum form is more closely tied to the particular quantum physical system. The definitions or categorizations of what information is quantum metadata and what information is quantum data can change from one application to another, or for different operations within the same application.
References herein to classical information include information that can be used by classical information systems. As such, this includes general classical information that is naturally or by its origin in a classical form and can also include quantum information in a classical form.
The method and system of the present teaching addresses a need for efficiently identifying entangled resources for optical measurements that use single photons. However, it should be understood that the teaching is not intended to be so limited. As understood by those skilled in the art, aspects of the teaching can apply to resources of numerous entangled systems including, for example, entangled atomic systems, ionic systems, spin systems, superconducting systems, quantum dots, and other systems. In these systems, the quantum state information, and associated quantum metadata concepts remain the same, but the physical system that carries the state, as well as, in some cases the different entangled bases, is different as understood by those skilled in the art. The present teaching can also be applied to hybrids of these and other types of systems.
Single photons are a powerful resource that carries correlated timing, phase and position information that can be used in a variety of quantum and/or classical systems that measure time, position, distance, phase and other related parameters. Specifically, it is known that interferometric systems can benefit from quantum optical states. For example, the Laser Interferometry Gravitation-Wave Observatory (LIGO), Light Distance and Ranging (LiDAR), optical coherence tomography, optical interferometric imaging can benefit from optical quantum states as can numerous optical image measurement systems. It is also understood that phase-sensitive correlation can be used to generate an image of an object from photons that have not interacted with the object when the photons that generate the image are correlated with other photons that do interact with the image. Entangled photons are particularly well suited to this task because of their inherent correlation properties. For entangle pairs of photons, one photon of the pair interacts with the object, and the other photon of the pair can be used to generate the image. Generally multiple pairs of entangled photons are used to create a multi-dimensional image. Thus remote, non-local imagers, such as the ghost imagers, can, therefore, also benefit from optical quantum states.
Single photons are indivisible particles and consequently their measurement is unique and well-defined. This leads to desirable features including privacy, security, tolerance to third party meddling and/or snooping, and quantization features useful for various communication, computing, and sensing applications.
At the same time, various optical sources are available and currently in development that can generate two, or more, entangled photons at a same time. For example, spontaneous parametric down conversion (SPDC) generates pairs of single photons at a same time. Some configurations of SPDC, for example, those that use forward and backward pumping, can generate four photons at a same time. Processes, such as four-wave mixing and Raman can also be used to generate pairs, triplets and/or quadruplets of photons that are all generated at a same time. In many cases, the time correlation is owed to time-energy entanglement processes. We may refer to these entangled sets of single photons as time-correlated photon sets or sets of entangled photons. There can be any number of time correlated photons in a set. A set of four entangled photons may be referred to as a quadruplet. Multiple sets of entangle photons are typically generated by an optical source over time. The number of sets per second is referred to as the generation rate. Spontaneous parametric down conversion sources, and many other down conversion and nonlinear sources can be configured to generate multiple sets of entangled photons over time. Some random or spontaneous processes generate streams of these time-correlated photon sets such that the time between arrivals of the time-correlated photons is governed by random processes and so the arrival times of these photon sets, and the inter-arrival time between photon sets, are correlated random values.
A common challenge with using the properties of the entangled time-correlated photon sets is that the time-correlated photons are typically surrounded in, e.g., time and space, by high levels of background photons, which is essentially noise. Low-cost sources, such as SPDC sources, typically generate more photons that are not time-correlated than are time correlated. Furthermore, photons are measured using detectors that produce substantial levels of background signals in addition to actual photon measurements. One feature of the present teaching is the ability to identify time-correlated photons amidst high levels of noise, photons from sources that are not correlated, and background signals with a minimum amount of computation and hardware.
Thus, one feature of the present teaching is that time correlations of entangled single photons having non-local properties can be exploited in measurement systems to achieve new functionality and/or improved performed metrics as compared to classical versions of these measurement systems and also as compared to known quantum versions of these measurement systems. In particular, using time correlations of entangled single photons according to the present teaching can achieve performance improvements in synchronization, reduction of noise and/or background resilience, and/or measurements of time and space that rely on quantum state information exchange. These performance improvements can be robust to high background counts.
Various sources support generation of single photons, including time-correlated single photons, that are entangled in various distinguishable bases. Entanglement refers to photons that share quantum state information such that measurements of each photon in one or more bases, even if performed at different times and/or places, yields measured quantum states in each basis that are perfectly correlated. Sometimes these states in each basis are referred to a superposition states. Example bases include time-energy, spatial position, momentum, polarization, wavelength and phase. For measurement applications, time-energy and phase bases are particularly useful.
Time-energy entangled photons possess a continuum of entangled time probabilities defined by their probability wavefunction, which we may refer to as a time wave packet. The probabilistic nature of the time-correlated value can be exploited if sub-wavepacket time resolution is used. By sub-wavepacket time resolution we mean time resolution less than a wave packet duration. Even with lower time resolution, the correlation can be exploited to find correlated photons precisely and/or within large background environments. In addition, many entangled photon generators rely on stochastic processes that are themselves random, allowing time-correlated photons to carry random time information based on those processes along with them. These features are exploited in various ways for measurement schemes that use embodiments of the time-correlated photon identification system and method of the present teaching.
Position-momentum entangled photons possess a continuum of entangled position probabilities defined by their probability wavefunction, which we call a position wave packet. The probabilistic nature of the position-correlated value can be exploited using sub-wavepacket spatial resolution is used. Even with lower spatial resolution, the correlation can be exploited to find correlated photons in space precisely and/or within large background environments. In addition, many entangled photon generators rely on stochastic processes that are themselves random, allowing position-correlated photons to carry random yet correlated position information based on those processes. These features are exploited in various ways for measurement schemes that use embodiments of the time-correlated photon identification system and method of the present teaching.
One feature of some embodiments of the system and method of the present teaching is the ability to identify time-correlated photons without relying on complex, high-resolution time synchronization schemes within the system sharing information. Numerous entanglement experiments use time coincidence counters to verify entanglement and validate the Bell inequality. These experiments rely on time coincidence for entanglement generated by spontaneous parametric down conversion as a valid determinant of entanglement and identification of photons that can carry other entangled state information. However, coincidence counters can be difficult to use in practice. In prior art systems, high-resolution time synchronization is needed. For example, even the length of the wire between the detector and the counter can skew timing. The future success of transition of quantum systems to practice demands systems and methods that can allow the use of quantum “coincidence” detection schemes that practically work in real life systems. The system and method of time-correlated photon identification of the present teaching can address many of these challenges. Some basic operations and examples of the use of time-correlated photons for the identification of quantum information are described in U.S. Provisional Patent Application No. 63/327,892, filed on Apr. 6, 202, entitled “Correlated Quantum State Identification System and Method”, which is incorporated herein by reference and assigned to the present assignee.
One feature of the present teaching is that it can use high-brightness single-photon sources to generate time-correlated photons. Some high-brightness sources create large numbers of quantum-entangled, time-correlated photons using Spontaneous Parametric Down Conversion (SPDC). SPDC relies on laser-pumped nonlinear crystals in various configurations. The pumped crystals emit photons that are time correlated. The crystals can also be configured to emit entangled photons in one or more basis which may include polarization, frequency (color) and/or spatial position. The state of a photon emitted in this multi-dimensional quantum state can be measured and represented as having an arrival time, a position, a frequency and/or a polarization.
One example case is a source that generates sets of four time-correlated photons. In addition to the quadruplets, these sources can also emit pairs and singles that are not part of a quadruplet.
It should be understood that the source 100 of
The source 100 can generate four photons simultaneously that emerge in particular directions, labeled a 110, b 112, c 114 and d 116 in
Some known sources that generate entangled photons can have those individual entangled photons emerge along a same path or within a same port. That is, all or some of the entangled photons in a set can emerge along a same or similar path and/or at a same port. This is true, for example with numerous waveguide-based sources, polarization sensitive sources and spatial mode sources. These individual photons of a set can be distinguished and/or later separated for individual measurement because they have e.g., distinctive polarizations, colors and/or spatial modes. As such, these sources can also be used in connection with the present teaching as would be clear to those skilled in the art.
In some embodiments, a metadata collector 120 is used to generate metadata about the quantum states. For example, the metadata collector 120 can be connected directly to the pump source 102 and/or to the optical output of the pump 102. The metadata collector can determine a pulse shape and repetition rate that can be used to determine time-windows where the entangled photons may be found. The metadata collector 120 can determine other information that relates to the quantum states generated by the interaction of the pump in the crystal 106, including for example, polarization, power, pulse width, amplitude and phase noise, and other information about the pump that contribute to the quantum states that are generated.
In some embodiments, the metadata collector 120 is collecting wavefunction information about the quantum states being generated in the crystal. For example, the metadata collector 120 determines specifics of the optical signals and the associated modes that pump the crystal 106 that yields information about when, where, and in what spatial condition, the entangled photons emerge from the crystal. As a simple, but important example, during time periods when there is no pump signal applied to the non-linear crystal, no entangled photons will emerge. Other examples of wavefunction metadata that can be collected include, for example, polarization, frequency, and phase properties of the photons as well as deterministic time windows of their emergence.
We may refer to pairs of a quadruplet that provide a higher probability of indicating a quadruplet as preferred pairs. We note that the description herein of high-fidelity indication of quadruplets by measurement of preferred pairs is provided for coincidences of photons that emerge from a crystal in different directions, forward and backward. Specifically, a forward emerging photon and a backward emerging photon are a preferred pair. However, systems and methods of the present teaching are not so limited. Generally, systems of the present teaching can utilize coincidence measurements of pairs of a quadruplet that herald that quadruplet with a high probability (preferred pairs) as compared to measurements of different pairs of that same quadruplet. This would be true, for example, for systems that had certain phase matching conditions that were specific to the quadruplet generation and not shared with phase matching conditions of pair generation. Additionally, some embodiments do not have preferred pairs generated, and/or do not use preferred pairs, and, thus, coincidence of any pair in the quadruplet can be used to identify the quadruplet. This can be done, for example, using sources that produce low background rates of singles and/or pairs together with producing quadruplets at a high rate.
One feature of the present teaching is that identification of pairs from a quadruplet can be used to identify all members of the quadruplet. This allows sharing of quantum information associated with measurements of photons in that quadruplet. The sharing can include exchanging of information from measurements of the entangled resources that is arranged in ordered lists. These lists can be the same or similar to lists that are used to identify entanglement and share quantum information using entangled pairs of photons. Some example identification methods and systems, and also associated applications that utilize identification, have been disclosed in U.S. patent application Ser. No. 17/465,235, entitled “Method for Synchronizing and Locking Clocks”, which is incorporated herein by reference and assigned to the present assignee. It is important to note that some embodiments of the present teaching do not generate lists at all, and rather the photon measurements and/or coincidence measurements are used in nominally real time or time offsets from real time, rather than being arranged and stored in lists for post processing. However, many properties of the elements of lists and associated correlation properties carry over to the real-time operation. Examples of real time operation can include a local finding of a coincidence pair in a set being used immediately or simultaneously to direct a measurement or read or store a value associated with measurement of another photon or pair of photons in that same set.
While configurations for identifying quadruplets based on pairs is described herein, the present teaching is not so limited to this description. Using the methods and apparatus of the present teaching, subsets of various numbers of photons of sets of various numbers of time-correlated photons can be used to identify the sets of time-correlated photons in various embodiments of the system and method for identifying time-correlated photons of the present teaching.
In the system 200, the source 202 produces four photons simultaneously. In some embodiments, two of the photons are directed to one location that includes the two detectors D1A 212 and D2A 214, and two photons are directed to a second location that includes two detectors D1B 216 and D2B 218. There is at least one local coincidence detector 220 at the location that includes D1A 212 and D2A 214, and a second local coincidence detector 222 at the location that includes two detectors D1B 216 and D2B 218. In some embodiments, the local coincidence detector can be as simple as a AND logic gate.
When the coincidence detector 220 finds a local coincidence at the location that includes D1A 212 and D2A 214 (in other words, determines there are simultaneous detection events at D1A 212 and D2A 214), a time-correlated photon pair has arrived. We note that the description assumes equal time-of-flight (TOF) from source 202 to detectors 212, 214, 216, 218 of each photon. The time correlation of sets of entangled photons ensures that when the location that includes D1A 212 and D2A 214 detects a local coincidence, the location that includes two detectors D1B 216 and D2B 218 will also detect a local coincidence. As mentioned before, much of the description herein assumes that latency from source to detector(s) is managed such that “coincidence” is synonymous with simultaneity.
As understood by those skilled in the art, various known approaches to addressing differences in latency from source to measurement can be used in keeping with the systems and methods for identifying time-correlated photons in distributed systems of the present teaching. For example, if the time-of-flight is longer on link 204 than 206, or link 208 than 210, the coincidence detector can be preceded by a fixed time delay in the connection between D1A or D1B to the coincidence detector. So more generally the concept of coincidence embodied herein allows for the use of known methods and systems at the receivers and receiver nodes that correct for any TOF, detection time, or any other differential latency in the system that is delivering and measuring the photons that carry the quantum correlated states. In fact, in some embodiments, systems and methods of identifying time-correlated photons can be used to determine and correct some latency differences from source to detector(s). That is, identifying time-correlated photons includes compensating for time delays in the determination of the coincidence. The time delays can include, for example time-of-flight delays of electromagnetic waves, detection latency, various circuit latency, optical measurement latency, etc.
Detecting a local coincidence at the location that includes both D1A 212 and D2A 214 means that two detectors D1B 216 and D2B 218 will detect a local coincidence. In some methods according to the present teaching, two locations construct ordered lists of measurements of time-correlated events that match without exchanging any classical data. No common quantum state basis is needed to identify coincidences. In some embodiments, times between arrivals of time-correlated photons is used to produce a shared random number, and there is no need to share any information between locations to accumulate the shared number. In some embodiments, measurements of additional entangled basis information carried by the time-correlated photons is shared information and there is no need to exchange any information between nodes to accumulate this shared entangled state information. For example, polarization and/or position information can be shared in this way.
In some embodiments, one or both of the coincidence detectors 220, 222 are connected to a processor 226, that can be one processor or multiple processors that can also be distributed. This supports the processor 226 generating event lists that include coincident determinations from one or both of the coincidence detectors 220, 222. Those lists may be formulated as time stamps, marks in time bins, or other formats. In some embodiments one or more of the detectors 212, 214, 216, 218 are connected to the processor 226 (only one connection shown). This supports the processor 226 generating event lists that include single photon detection measurements, that would typically also include background counts events, of the one or more of the connected detectors 212, 214, 216, 218. Those lists may be formulated as time stamps, marks in time bins, or other formats. Those lists may be in order of arrival time, as referred to as ordered event lists or lists of ordered measured events.
In some embodiments, one or more of the photon sources 202, one or more detectors 212, 214, 216, 218 (only one connection shown), one or two coincidence detectors 220, 222 (only one connection shown) can be connected to a metadata collector 224 that is connected to processor 226. This supports the processor 226 generating metadata information lists. The lists can include, for example, one or more of number of coincidences in a time window, time-windows of expected entangled pairs based on pump pulse information, background counts or expected background levels based on detector bias point, measurement start and stop times in some coordinated time frame, quantum state coherence levels (including deterministic and probabilistic values or estimates), various wavefunction information, and many other kinds of information.
A distinction is made between metadata, which is information about the quantum states, and quantum state measurement information or values (quantum data), is that a quantum measurement collapses the quantum state, whereas metadata can be collected without collapsing the state. As one example, this feature allows the quantum privacy of a superposition basis of an entangled system to be kept locally, while the other information is shared publicly to support privacy and security applications. As another example, this feature allows multiple different kinds of entanglement sharing applications to identify entanglement while sharing small amounts of data about the entanglement. In some cases, the measured quantum state information can carry a high capacity of information, if it is part of a high-dimensional quantum basis, and the information exchanged to “tap” this capacity can be small. As one particular example, a number of coincidences, which is a single number, can be used to verify many precisely measured time-entangled photon (or even just one). For example, the resulting shared timestamp values that represent the measured quantum state value of these entangled photons can represent a lot of information, as depends on the application.
It is important to note the generality of the sharing of the metadata and the sharing of the quantum entangled states according to the present teaching. Different applications would be constructed and would use different combinations of these measurements, lists and sharing methods in different ways. Some examples are presented herein. However, it will be clear to those skilled in the art that numerous systems and methods can benefit from and use the association of the metadata and the measured quantum state data to share and derive quantum entangled state information. For example, the method and system according to the present teaching is applicable to distributed systems, localized systems and hybrids of localized and distributed. The method and system can be applied to privacy systems, key distribution systems, measurement systems, coding and communication systems, location systems, synchronization systems and many other kinds of systems that use entangled quantum state information. Embodiments of the system and method that use the associated metadata can, for example, help reduce information sharing requirements, enhance privacy and security, improve accuracy, reduce latency, and/or support high background count operations while sharing quantum state information as compared to systems that rely on sharing of quantum state information alone.
In some embodiments, lists of measurement event information generated in two separated locations that is associated with the coincident photons determined in each location is shared information between those locations with no classical information exchange. The lists can include, for example, arrival times of coincidence photons. The lists can be ordered by time of arrival. Time can be secretly shared because no classical time information is shared between the nodes.
Additionally, latency can be reduced since there is no waiting for a classical exchange to find coincidences or to otherwise establish the time-correlation and/or phase-correlation property and associated shared time and/or phase information of a photon that belongs to a quadruplet. Most practical systems will benefit from “starting” the accumulation of both lists at roughly the same time (as determined by a common reference). However, since coincidences in real systems tend to occur at low rates (e.g., milliseconds), the accuracy of this “start” time can be low. Importantly, in some configurations, simple free running clocks can be used in each location. In some configurations, a common time reference and/or start time can be resolved simply by energizing, shuttering, or otherwise time-stamping the entangled source until ready to effectively “start” both lists at the time entangled photons start to arrive at both locations.
In some embodiments of the present teaching, the state dimension of the time basis is dependent on the clock resolution at each detector pair. The clocks can be running at nominally the same rate, to an accuracy that provides a desired resolution. If the time basis is a time between arrivals, delta-t, absolute time is only relevant to insure both detectors start their ordered list with the same event making absolute time irrelevant and clock accuracy requirements only relevant for short inter-arrival times. Not requiring accurate absolute time and synchronizing of absolute time is highly advantageous for many applications.
One feature of the present teaching is that the amount of classical information shared between locations can vary as desired or required by a particular application. In some embodiments, the classical information shared is the quantum metadata that is quantum data in a classical form associated with the quantum state information. Varying the amount of classical information shared can also be expressed as varying the level of classical isolation of the two locations. For example, the isolation can be complete, with no classical information shared, or the isolation can be partial with some information shared depending on the particular application. As described above, by using coincidence of pairs of quadruplet time-correlated photons, time and other quantum state information can be shared between locations without any need to send any classical information about the measured states. In various embodiments, different amounts of information about the measured quantum states, and associated lists of measured state information can be shared. Information about the measured quantum states that is not a value of one or more of the measured states may be referred to as metadata as described herein.
Systems using time-correlated photons look for coincidences in time at two different detectors. The background events align in time at different detectors only by chance. For uniform background arrivals with a known rate, it is possible to calculate the probability that these background events align in time. To the extent a reference time exists between nodes and flight and detection time latency from source to detector are taken into account, the arrival time of time correlated photon events 236, 238 in the two lists 232, 234 is the same. Regardless of relative time, time correlated photon arrival events occur with exactly the same time difference (within measurement error) between events if the two clocks run at the same rate. As such, by sliding and comparing the two lists as a function of time, represented by arrow 242, relative time between the two detectors can be determined. By sliding we mean comparing the two lists at each of a series of different time shifts between the two lists. By comparing we mean adding the number of matches per relative time position of the shift. So together by sliding and comparing we are able to generate a cross-correlation of the two lists.
A peak, with nominally the value of all the time-correlated photons (six in the example) will result at the matched position caused by the sliding, and be lower at other relative time position. The sliding and counting matches at various positions can provide a cross-correlation of the two lists 232, 234. As understood by those skilled in the art, cross-correlation can determine a similarity between two data sets, or two lists of events.
In some methods, coincidence event lists 244, 246 are generated. These may be generated, for example, from the output of the coincidence detector 220 and coincidence detector 222 described in connection with
In methods where the reference time and/or clock rate synchronization is unknown, these lists can be shared, and a slide and compare operation, which is represented by arrow 252, can be performed on the coincidence event lists 244, 246 to provide information to synchronize clocks in the two locations. See, for example, U.S. patent application Ser. No. 17/465,235 entitled Method for Synchronizing and Locking Clocks, which presents additional details, applications and systems and methods for sharing quantum information using event lists.
In some methods, coincidence counts 254, 256 are generated. This kind of information about the measured events having no state value information is referred to herein as quantum metadata because this type of metadata is related to quantum state information, but does not contain any actual measured quantum state information. This quantum related metadata can be a number of the coincidence counts in a set time window generated at the output of the coincidence detector 220 and coincidence detector 222, which was described in connection with
One set 298 of entangled photons includes four photons 261, 261′, 261″, 261′″. The set 298 of four photons 261, 261′, 261″, 261′″ is shown aligned vertically to suggest how they are time-correlated, that is they originate at a common time. The other set 299 of entangled photons includes four photons 262, 262′, 262″, 262′″. The other set 299 of four photons 262, 262′, 262″, 262′″ is also shown aligned vertically to suggest how the photons 262, 262′, 262″, 262′″ are time-correlated, that is they originate at a common time. The common time for the two sets 298, 299 is different since they are generated at different times. It should be understood that background photons, while commonly present are not shown in the diagram 260 for clarity.
One feature of the present teaching is the recognition that the set 298 of four entangled photons 261, 261′, 261″, 261′″ are all correlated in time and so one pair 263 of photons 261, 261′ of the set 298 of four entangled photons being correlated in time indicates that all four photons 261, 261′, 261″, 261′″ of the set 298 of four entangled photons are entangled. This is an important feature that allows, for example, exploitation of the non-local and/or high precision features of the time correlation that crosses all four photons 261, 261′, 261″, 261′″. This is possible because sets 298, 299 of four entangled photons that are time correlated can be determined by coincidence determination of only two photons in the set. For example, coincidence of pair 263, and/or coincidence of pair 267, identify set 298. Likewise, coincidence of pair 265, and/or coincidence of pair 268, identify set 299. This identification then enables the exploitation of some or all of the entangled state information that is carried by the set 298, 299. That is, just determining that a pair is correlated indicates that all four photons are correlated. More generally, determining a subset of photons in an entangled set is correlated indicates another subset, or subsets, of the same set are correlated.
As such, some embodiments of a method of the present teaching determine a coincidence of the one pair 263 of photons of the set 298 of four entangled photons 261, 261′, 261″, 261′″ and also detect at least one photon 264/261″ that is not in the pair 263 of photons of the set 298 of four entangled photons 261, 261′, 261″, 261′″. The detection of the one photon 261″ can be, for example, a simple indication that a detection event occurred. The indication may be a mark in a time bin associated with the detection of the photon 261″. The detection can be configured to generate additional state information about the photon 261″. For example, a detection event can include additional measured quantum state information carried by the detected photon, including a precision time of arrival, polarization, wavelength, phase and/or position of the detected photon. This additional state information can be realized, for example, if the quadruplet is hyper-entangled in multiple bases, and the detection event is made appropriately sensitive to the hyper-entangled bases.
By detecting a photon, we mean generally making a measurement of one or more of the quantum states being carried by that photon. An example of detecting is one or more of measuring a time of arrival of a single photon, measuring a polarization of a single photon, measuring a wavelength of a single photon and/or measuring a position of a single photon. Measuring single photons can be done using known single photon detectors, including various photo multiplier devices, avalanche photodiodes, Geiger mode detectors and other single photon detectors. Other state information can be determined in the measurement, for example using various optical analyzers before a single photon detector or detectors. Thus, detecting one or more properties of a single photon can require use of more than one single photon detector. Importantly, a detection of a single photon is a singular measurement event and all properties that are derived from that measurement event are tagged to that particular photon. In this way, a so-called detection of a photon can produce multiple state values.
The method continues by determining that the at least one photon 264 from the other pair 267 of the set of four entangled photons 261, 261′, 261″, 261′″ is entangled using the coincidence of the one pair 263 of photons of the set 298 of four entangled photons. Thus, the entanglement of the set 298 of four entangled photons is identified from the coincidence of the one pair 263 of photons of the set of four entangled photons.
Stated another way one aspect of the present teaching is the highly useful concept that knowledge of entanglement of all four photons can be determined from the detection of only two. This capability serves to separate, or make independent, an identification of an entangled set of photons, and other measures of quantum state information of at least some other photons in the set of entangled photons. For example, it is possible that some photons in an entangled set are used to identify the entangled set, and other photons are used to derive or exploit other quantum information of that entangled set. That is, once an entangled state is identified by determining coincidence of pair 263, it is possible to exploit entangled quantum state information that is carried by, for example, the single photon 264 after its measurement or, more generally, any other subset of photons in the set 298.
The identification method can be used, for example, in a system where the determination of the coincidence of pair 263 is used to herald the entangled photon 264. The identification can be used, for example, to synchronize a clock that is part of or connected to a system that is determining the coincidence of pair 263 and another clock that is part of or connected to a system that is detecting the photon 264. Numerous synchronization configurations and performance parameters can utilize this method.
The identification method can be used in real time or essentially real time, assuming sufficient attention is given to delays and time-synchronization for both the coincidence determination and the photon measurement/detection. The identification method can also be used in non-real time. In non-real-time systems, measurements are made at one time or over different times, and then subsequently analyzed and/or compared. Time-correlation identification and entangled state information derived from the combination of the coincidence determination and the detected photon 264 are determined and/or exploited at some point after one or both of the measurements are completed. This can be done if the information about the coincidence determination and/or the detection events are kept in lists that represent the measurement events or contain the measurement information that is pertinent to identification. The lists are then subsequently used for analysis and/or comparison to identify entanglement and/or to determine quantum state information.
In some methods, the pair 263 is sent to one location, measured and processed to determine coincidence in one location and the other photons in the set 298, including at least the detected photon 264, are sent to a different location for the detection. In these cases, the lists containing measured event information that are generated in the two locations can be shared or exchanged, e.g., over a network or other classical communication link.
In general, various lists described in connection with the present teaching, such as, for example, the lists described in connection with
Key features of the generated lists can be understood by distilling down to just two entangled set elements shown in the diagram 260 of
Some embodiments of the method of the present teaching generate a set 298 of entangled photons 261, 261′, 261″, 261′″, and then determine a coincidence of one pair 263 of photons 261, 261′, and detect one photon 264 of the other pair 267. It is therefore determined by the coincidence event that the detected one photon 264 of the other pair 267 is entangled in the set 298. As such, the determination of coincidence of pair 263, which can potentially be completely independent of the detection event of detected photon 264, identifies that entanglement status. This same process is repeated for the other set 299 of photons 262, 262′, 262″, 262′″. The set 299 is generated, a coincidence of one pair 265 of photons 262, 262′ is determined, and a measurement of a photon 266 of the other pair 268 of the set of entangled photons 262, 262′, 262″, 262′″ is performed.
After generation and measurement of both sets 298 and 299 of photons, based on the determined coincidences, a first list of state values corresponding to both the identified set 298 of four entangled photons 261, 261′, 261″, 261′″ and also the identified other set 299 of four entangled photons 262, 262′, 262″, 262′″ is generated. In this simple two-set example, the list can include, for example, two entries that are a determined coincidence time for each set 298, 299. This list can be presented or stored in numerous ways. The list can be marks in regularly spaced time bins that indicate the time-bin corresponding to when the coincidence determination is made. The list can also, or in addition, be presented as timestamps of the coincidence determinations. The list can also, or in addition, include additional state values, such as the difference in arrival time between the two determined coincidences, a polarization value, a wavelength value, a spatial position, or a phase value associated the pairs 263, 265. Lists can also be generated to include measured values of some or all of the individual photons 261, 261′, 261″, 262, 262′, 262″ as dictated by the application. The particular content of a list can be based on the particular application's need as well as the specific system and method used for the measurements, detections and coincidence determinations.
One feature of the present teaching is that two, potentially widely geographically separated and/or classically isolated, coincidence determinations of different pairs in a set of entangled photons provide an effectively latency free, or non-local, sharing of quantum information carried by (or contained within) the entangled set. Thus, a determined coincidence of the other pair 267 of photons 261″, 261′″ of the set 298 of four entangled photons 261, 261′, 261″, 261′″ identifies the entanglement of the set 298 of four entangled photons 261, 261′, 261″, 261′″ and a determined coincidence of the other pair 268 of photons 262″, 262′″ of the other set 299 of four entangled photons 262, 262′, 262″, 262′″ identifies the entanglement of the other set 299 of four entangled photons 262, 262′, 262″, 262′″. A second list of state values corresponding to both the identified set 298 of four entangled photons 261, 261′, 261″, 261′″ and also the identified other set 299 of four entangled photons 262, 262′, 262″, 262′″ is generated that is based on the determined coincidence of the other pairs 267, 268.
This second list is based on measurements of different pairs than the first list, however, the first list of state values and the second list of state values are correlated. That is, a first list is generated by measurements of pair 263 of photons 261, 261′ of one set 298 of entangled photons 261, 261′, 261″, 261′″ and by measurements of pair 265 of photons 262, 262′ of the other set 299 of entangled photons 262, 262′, 262″, 262′″. The second list is generated by measurements and coincidence determinations of the other pair 267 of photons 261″, 261′″ of one set 298 of entangled photons 261, 261′, 261″, 261′″ and by measurements and coincidence determinations of the other pair 268 of photons 262″, 262′″ of the other set 299 of entangled photons 262, 262′, 262″, 262′″.
In some embodiments, these measurements of the detections and coincidence determinations that contribute to the first and second lists are performed in one localized node and/or with one clock providing timing. In other embodiments, these measurements of the detections and determinations are performed in more than one node and/or with more than one clock providing timing.
One feature of the present teaching is that the hardware and processing needed to determine coincidence and/or measure state information of photons can be constructed using relatively simple and low-cost components.
Some embodiments of the time-correlated photon identification system of the present teaching use an AND logic gate and processing to determine shared quantum information from time-correlated quadruplets.
In some embodiments a BBO crystal 328 is energized with a pump laser beam 330 that is reflected back at the BBO crystal 328 by a mirror 332. The resulting output along directions of a, b, c, and d includes various singles, doubles (pairs) and quadruplets that are time correlated photons. The allowed states of this system are as follows: 1) random single photons at arbitrary times at a, b, d, and c; 2) two-way coincidences at a and b only; 3) two-way coincidences at d and c only; and 4) four-way coincidences at a, b, d and c. Excluded states of this system are as follows: 1) two-way coincidence at a and c without a coincidence at d and b; 2) two-way coincidence at b and d without a coincidence at a and c; 3) three-way coincidence at a, c and d without a coincidence at b; 4) three-way coincidence at a, c and b without a coincidence at d; 5) three-way coincidence at d, b and a without a coincidence at c; and 6) three-way coincidence at d, b and c without a coincidence at a.
In this embodiment of the system 300, by carefully choosing the pairings of a, c, d, and b from the source 302, we can guarantee with a high likelihood that if a and c see a coincidence, d and b will see a coincidence.
There are various ways to compensate for lost time-correlated events. For example, various methods for compensating for lost time-correlated events include using a classical channel for error detection and/or correction. However, unlike a two-way entangled situation, a classical channel can be used to detect and/or correct these errors with a minimum of information exchange (low bandwidth) for time-correlated quadruplets.
In one method of error correction and/or detection, nodes 328, 330 keep a running count of coincidences and periodically share their numbers through a classical channel. This is a type of parity error checking and correction but does not require the use of additional signal. In one method, the numbers do not match, the nodes 328, 330 know photons have been missed. The nodes 328, 330 know that the difference between counts equals the number of missed photons, and the detector with the lower number is the one with missing counts. One bandwidth-efficient method to manage this would be to exchange counts at a rate approximately equal to the expected loss rate making the probability of a single lost photon during a counting interval equal to 0.5. If the counts match, the lists necessarily match. If the counts do not match, at least one missing photon case is identified.
If there is a missing photon, both nodes 328, 330 could purge their lists for the interval since the last matching count exchange as a way of improving accuracy. Alternatively, nodes 328, 330 could exchange their counts for half the list, and see if the counters match. If the counters match, then each node tries for three-quarters of the list. If the counters do not match, then each node tries for one-quarter of the list. Successively cutting the remaining list in half, or doubling it, until the counts match, allows identification of additional time-correlated photons that might otherwise be discarded.
There are many other ways to detect and correct errors with a low information rate classical exchange. For example, the nodes 328, 330 could share polarization values, but keep time of arrival as a shared secret. This is highly valuable given the large state dimension that can be realized with time. For example, time can be measured to very high accuracy, for example, picosecond or higher. As such, a value with many digits of precision can be shared for each measured entangled set as compared with polarization, which may have only two bits of precision. If polarization values do not match, the most likely reason would be a lost photon as described above. Because both these bases are carried by the same entangled photon set, low-bit value polarization values can be used to improve the accuracy of the large number of bits time value sharing.
As another example of a method of detecting and correcting errors, 328 and 330 can share their list of coincidence event time stamps or combs. Any missing coincidences are discarded. As yet another example of a method of detecting and correcting errors, quantum metadata that is wavefunction data that indicates particular time windows where entangled photons are not generated is used to discard any measured state values that are found in that window.
The various approaches for determining an error condition, including lost photon error conditions, and correcting those error conditions described herein are general, and apply whether the measured photons and/or determined coincidences processes are performed in a same location or different location. As such, they can apply to the various embodiments of entangled state identification for quantum imaging described herein, including those embodiments described in connection with
One feature of the present teaching is that it can be easy and cheap to build a local coincidence detector that is very accurate in measuring coincidences in short time windows. This measurement accuracy will drive the error rate due to false entanglement low. The more likely errors in time correlated quadruplets are related to lost photons. If loss is low, it is possible to build a system with no classical channel between nodes 328, 330. If loss is higher, it is possible build error detection and correction schemes that share information between processors 320, 324 in nodes 328, 330 that require only a very low information transfer rate, as compared, for example, to systems that exchange information using pairs of time correlated photons only.
The probability of error caused by singles arriving simultaneously (false coincidences) at D1A 312 and D2A 314 or D1B 316 and D2B 318 is limited by the speed of the local coincidence detector which effectively determines the equivalent resolution of time stamps or size of time bins. The exact formulas have been derived for pairs, see, for example U.S. patent application Ser. No. 17/465,235, entitled “Method for Synchronizing and Locking Clocks”. Low cost, high speed AND logic gates which can be used to detect coincidence are widely available, for example, the 74VHCT08A from Fairchild Semiconductor is specified to run at 5 ns and costs $0.10. With a 5 ns window, the expected value of a false coincidences per second (false entanglement) in a system generating 10,000 singles per second is given by:
When two detectors are co-located, a simple logical AND condition can determine coincidences with high time resolution. When the two detectors are remote from each other, we can exchange a quantum state comb over a classical channel to find coincidences. A quantum state comb (hereinafter “comb”) is an ordered list of measurement events. That is, a comb is a list of measured states in the order they arrive at a measurement node and/or a particular detector or group of detectors in the measurement node. A comb can also be an ordered list of measured events from different spatial positions. Also, a comb can be an ordered list of measured events from different polarizations or from different colors. Also, combs can be a combination of measured events that include any combination of the above and any other type measured events.
The comb time can be measured from various bases, such as a local clock, which can be synchronized in a relative and/or absolute basis to a non-local clock. The local clock can be a free running clock that is synchronized using shared entanglement via methods described herein. It should be understood that a comb includes more than one value per measured state. The value can be, for example, polarization, arrival time, frequency/color and/or spatial position. This is the case, for example, if an entangled state is a hyper-entangled state, where a single photon of a pair or set is entangled in more than one way (dimension or basis). In some embodiments, different members of a comb have different values. That is, a comb can include more than one type of entangled state where the more than one types of entangled states are not entangled with each other. This could be the case, for example, if quantum states from two different sources generating entangled states were multiplexed. This could be done, for example, to increase the rate of entangled pairs being generated.
The method requires exchanging information that includes singles and coincidences then sliding the combs past each other to find the maximum number of overlaps (e.g., cross correlation). Since many practical entanglement sources produce singles at a rate that is three or four orders of magnitude greater than the coincidence rate, a large amount of information must be exchanged and processed, most of which consists of background noise in the form of singles.
For example, if a given source has a singles rate of five thousand per second, and a coincidence rate of ten photons per second, then five-thousand-ten events must be exchanged over the channel per second of data collection. Subsequent processing involves sliding the two combs past each other. That process requires a number of comparison steps that is equal to the 1/(time resolution)×(2×the clock uncertainty between the two detectors). As an example, if the time resolution was 10 ns, and the clock uncertainty was 100 microseconds, the step count would be 1/10 ns×2×100 ms=20 million comparison steps. By contrast, if only coincidence information is exchanged, the step count would be eleven.
In this embodiment, the table 350 described in connection with
For example, two detectors 404, 406 can be connected to an AND gate in processor 412 and the other two detectors 408, 410 are connected to a different AND gate. When the outputs of the two AND gates are both high because photons are present at all four detectors 404, 406, 408, 410, a time-correlated quadruplet is identified. This assumes equal time-of-flight from source to detectors and through AND gate outputs. It is understood that unequal times of flight can be addressed in various known ways.
We note that if the outputs of the two AND gates are provided to another AND gate, when that third AND gate is high, it correctly identifies the presence of a time-correlated quadruplet. This is true regardless of which pairs of detectors 404, 406, 408, 410 are connected to the AND gates. By putting outputs from detectors coupled to a front side (a or b) and a backside (d or c) into the same AND gate, it reduces the number of AND gate high counts, because the probability of singles appearing at the same time from the front and back directions is low. This can reduce the number of false identifications of time-correlated quadruplets based on a single AND gate connected to just two detectors being high. In some embodiments, this eliminates the need for a third AND gate to identify a time correlated quadruplet.
In this configuration, quantum metadata that is wavefunction data that indicates particular time windows where entangled photons are not generated can be used to discard any measured state values that are found in that window. This can be realized by having a metadata collector (not shown) that generates a “high” signal during time windows were single photons are generated, and a “low” signal otherwise. Taking this metadata signal and putting it into an AND gate into processor 412 with any or all of the inputs from detectors 404, 406, 408, 410 can prevent false positives.
One feature of the present teaching is that two photons in a set of entangled photons, which can be a quadruplet set, can be used to perform known entanglement functions. One useful application ghost imaging. Ghost imaging using pairs of photons is a known application that requires a plurality of entangled photons to be used as illumination and image photons. In connection with the system and method of the present teaching, if two photons in each of a plurality of sets of photons are used to formulate a ghost image, then the other photons can be used to identify the entangled set, or be used to improve performance of the ghost image system. For example, two photons of a set can be used for ghost imaging, one to provide the image but not in a path with the item being imaged, and the other used to illuminate the item. One or two other photons from the set are detected and the detected signals processed and used, e.g., for identifying the entangled set. In some embodiments, identification of the entangled set can be said to herald a particular ghost image measurement event as a pair without needing to access the photons of the pair.
Ghost imaging generally works with single photon arrivals measured in a single detector in positioned after a mask providing image information about the mask based on coincidences with paired single photon arrivals measured using a spatial sampling system positioned at a different location that is not in the path of the mask. There are different known configurations to implement ghost imaging, and the similar ghost masking systems. See, for example, Y. Shih, “The physics of ghost imaging,” in International Conference on Quantum Information, paper QTuB1, Optica Publishing Group, 2008, and related publications by the same author. In embodiments including ghost imaging measurement of the present teaching, the arrival times of pairs participating in a ghost imaging path improve the measurement fidelity and speed. Specifically, this independent determination of arrival time, or identification of time-correlated pairs, can lead to improved image fidelity, imperviousness or tolerance to background, faster acquisition times, simplified operation and/or other beneficial features as compared to prior art ghost imaging that relies only on pairs.
Light coupled from direction a is coupled to a detector 506. Light coupled from direction d is coupled to a detector 508. Light coupled from direction c is coupled to a path that includes two imaging lenses 510 and 512 and an object 514.
Different embodiments can use imaging systems other than the two lens 510, 512 imaging system shown in
Light from direction b is coupled to a path that includes a spatial sampling system 518. In some embodiments the spatial sampling system 518 is a two-dimensional array of single-photon-resolution detectors 520, 520′, 520″. In some embodiments (not shown), the spatial sampling system 518 includes an optical fiber coupled to a single photon detector that serves to spatially sample an x-y plane with translation. Thus, the photons from this path are detected with a spatial resolution that is capable of resolving detail in the image formed in the path from direction c. However, there is no imaging system in this path. The photon detections are received as a function of time, and their timing, and optionally their phase properties are recorded.
In embodiments having a two-dimensional array of single-photon-resolution detectors, each detector 520, 520′, 520″ has an output connected to a processor 522. The processor 522 can include AND gates 524, 524′, 524″, 528, 530 used to determine photon coincidences measured by detectors 506, 516, 508, 520, 520′, . . . , 520″. As described herein, two-input AND gates produce a “high” signal at an output when pairs of detectors connected to two inputs detect photons simultaneously. Outputs from each detector 520, 520′, 520″ in the detector array 518 are input to one input of corresponding AND gates 524, 524′, 524″. Outputs from the detector 516 in that path with the object 514 are provided to the second input of each AND gate 524, 524′, 524″ connected to a detector in the array 518. Outputs of the AND gates 524, 524′, 524″ are provided to a processor 526. Ghost images are produced by the processor as the pattern of detector positions in the array 518 that have photons coincident with the detector 516, that results from the one-to-one spatial correlation of correlated photon pairs. This pattern, and related ghost image, can be determined by processor 526 based on the signals provided by the AND gates 524, 524′, 524″. As in traditional ghost imaging, if the AND gate processing between the bucket detector 516 and the array detectors 520, 520, . . . 520″ is not performed, the signal from the array 518 would look nominally “white”, as background counts would be measured at individual detectors 520, 520′, . . . 520″.
In addition to the traditional ghost imaging measurement, signals from detector 506 and/or detector 508 are used to help identify correlated pairs. The output of detector 506 is provided to one input of the AND gate 528. The other input of the AND gate 528 is connected to an output of detector 516. The output of detector 528 is provided to one input of AND gate 530. The other input of AND gate 530 is connected to all of the outputs of detectors 520, 520′, 520″. The outputs of the AND gates 528 and 530 are provided to the processor 526. The processor can process the outputs from the AND gates 524, 524′, 524″, 528, 530 in numerous ways. For example, the “high” signal from one or both of AND gates 528, 530 can be used as a trigger or marker to look for a coincidence-indicating “high” signal from one or more of AND gates 524, 524′, 524″. These embodiments that include processing of the signals from detector 506 and/or detector 508 provide, for example, robustness to background photons of the ghost imaging system.
In some embodiments, an optional second object 532 and associated imaging optics (not shown) can be placed in the path in front of a detector 508. In this case, a second ghost image of the second object 532 can be measured. In addition, composite images can be measured of both objects 514, 532. In general, various combinations of images can be realized, based on the pattern of coincidences that are determined by the processor 526 and based on the outputs of the AND gates 524, 524′, 524″, 528, 530. Similarly, an additional object and imaging optics can be placed in front of detector 506 to provide adaptable composites of three objects' images.
Many sources of quadruplet, triplet or dual entanglement also emit single uncorrelated photons at high rates that may be two or more orders of magnitude greater than entangled photons. Other sources of uncorrelated signals that manifest as single counts can be noise sources such as light in a room, or natural light from the sun and other background photon sources. It is advantageous in many applications to use low-cost sources of entanglement that emit large quantities of singles. It is also advantageous in many applications to operate outdoors in daylight or in strong artificial light.
The single uncorrelated photons from many of the common background sources occur at random intervals. If these random intervals overlap within the time resolution of detection hardware, AND gates or other coincidence detecting processors, they can be miscategorized as entangled photons. Since these uncorrelated photons are generated at statistically independent times, the probability of this mis-categorization is the product of the probability of an uncorrelated photon arriving within a given time resolution raised to the power of the number of photons per set, which also corresponds in some embodiments to the number of detectors.
Thus, for pairs entanglement, the error is proportional to the probability of an uncorrelated photon arriving within the time resolution squared, for triplet's entanglement, the error is proportional to the probability of an uncorrelated photon arriving within the time resolution cubed, and for four-way or quadruplets entanglement, the error is proportional to the probability of an uncorrelated photon arriving within the time resolution to the fourth power. As such, interferometric measurement systems of the present teaching reduce the probability of errors in identification of a valid measurement point exponentially with the number of additional photons in the entangled set that are determined coincident with the measurement point photons. As such, in the imaging system 500, the AND, or coincidence detection 530 of detector 508 and the imaging detectors 520,520′, 520″ reduces error. Furthermore, adding AND, or coincidence detection 528 of detector 506 reduces error even further.
As a numerical example, the probability of accidental coincidence in a microsecond window for a pair of detectors with random arrivals of 100,000 background photons per second at each detector is 1%. Three accidental coincidences probability is 0.1%, and four-way accidental probability is 0.01%.
One feature of the present teaching is that heralding of coincidences using the sets of entangled photons that number more than two allows two separate nodes to independently find coincidences so that the correlated imaging can be provided in remote locations.
Light from directions a and c are sent to one node 554 and light from directions b and d are sent to a second node 556. Light coupled from direction a is coupled to a detector 566. Light coupled from direction c is coupled to a path that includes imaging lenses 560, that can be two lenses on either side of an object 558. The object 558 can be any object of which an image is desired to be determine. In some embodiments the object 558 is a mask that blocks or passes light so as to form a two-dimensional pattern. In some embodiments, the object 558 is a three-dimensional object that blocks or passes light.
A detector 564 is positioned behind the imaging lenses 560 and object 558. This detector 564 can be referred to as a bucket detector at least in part because it accepts photons from the full image plane that corresponds to the object plane of object 558. An AND gate 568, or other coincidence determination system, is connected to the outputs of detectors 566, 564 and the output of the gate 568 input to a processor 570. In some embodiments, the processor 570 generates an ordered list of coincidences based on the output of the AND gate. The lists can be, for example, timestamps of coincidences, and/or coincidence events in time bins.
Light from direction d is coupled to a path that includes a spatial sampling system 572. In some embodiments the spatial sampling system 572 is a two-dimensional array of single-photon-resolution detectors 574, 574′, . . . 574″. In some embodiments (not shown) the spatial sampling system 572 includes an optical fiber coupled to a single photon detector that serves to spatially sample an x-y plane by being moved. Light coupled from direction d is coupled to a detector 576. Each detector 574, 574′, . . . 574″ has an output connected to a separate AND gate 578, 578′, . . . 578″. Detector 576 is connected to another input to all of these AND gates 578, 578′, . . . 578″. High signals from these AND gates 578, 578′, . . . 578″, indicating a coincidence at the respective detector are collected by a processor 580 that, in some embodiments, generates one or more ordered list of coincidences. The lists can be, for example, timestamps of coincidences, and/or coincidence events in time bins. The ordered lists can be, for example, a single ordered list of coincidences, where each position of the spatial sampling system that corresponds to the coincidence is indicated in the list. The ordered lists can also be, for example, individual lists for each position of the spatial sampling system. The ordered lists can also be combinations of these.
The lists generated by processors 570, 580 can be shared over a classical channel that can be any of a variety of known communication channels. Lists can be shared in either direction to and from nodes 554, 556. One example is a list from processor 570 is sent to processor 580. By comparing a list of coincidences generated by processor 570 to the list or lists generated by processor 580, assuming at least some of the members of the lists contain measurements of photons that are generated in the same time window, and therefore can be entangled, it is possible to produce an image of the object 558 at the remote node 556.
One feature of this image generation is that it is not possible to generate that image from information sent on paths b and d and the classical channel 582. The list generated by processor 570 has no clear connection to the object. The image only manifests when locally detected coincidences in node 556 are compared with coincidences in node 554. For example, by comparing the list from 570 that is sent to node 556 with the list or lists generated by processor 580. That is, ghost images are produced as based on the pattern of detector positions in the array 572 that have photons coincident with the detector 564, that results from the one-to-one spatial correlation of correlated photon pairs. This pattern, and related ghost image, can be determined by processor 580 based on locally generated list(s) from AND gates 578, 578′, . . . 578″ and a list received from processor 570 generated based on signals from AND gate 568.
The processor 632 can produce an image of the object 616 in response to a plurality of measured coincidence events as in traditional ghost imaging. However, this image will be affected by false coincidences that may be the results of dark counts and/or background photons impinging on detector D3 and spatially sensitive detector D4. By also including comparison with coincidences determined by coincidence detector 628, false coincidences measured by coincidence detector 630 can be eliminated, thereby producing an improved image of the object 616. One feature of this configuration as compared to traditional two-entangled photon versions of ghost imagers is that less expensive, lower performance, and/or higher background detectors with less spatially sensitive detectors can be used.
Another photon from the same entangled set is sent to an imaging system of lenses 722, 724 and object 726 and is detected by a detector D3728 whose output is connected to coincidence detector 740. Another photon from the same entangled set is sent to an imaging system of lenses 730, 732 and object 734 and is detected by a detector D4736 whose output is connected to coincidence detector 740. The objects 718, 726, 734 can be the same or similar objects and/or they may be different objects. A processor 742 can compare coincidences between spatially sensitive detector D1712 with various combinations of detectors D2720, D3728 and/or D4736 to generate different images that are based on some combination of objects 718, 726, 734. For example, four-way simultaneous coincidences combined with the spatial sensitivity of D1712 can produce a composite image of all three objects. Also, for example, three-way coincidences of spatially sensitive detections from D1712 and any two of detectors D2720, D3728 and D4736 can produce a composite of the two objects in the path of the respective two detectors. It should be understood that various combinations are possible. This kind of imaging system can produce similarity and difference data on the various objects as well as various combinations of objects. As a simple example, if objects 718 and 726 are masks that do not share any common transparency, then there will be no coincidences of D2720 and D3728, and therefore D1712. As another example, a mask object 734 can be configured to find similarity between masks 718, 726 in different regions, because only when all three mask regions pass (or block) photons will coincidences (or lack of coincidences) be registered at D1712. Various combinations of coincidences, combined with various combinations of masks are possible as understood by those skilled in the art. In addition, larger sets of entanglement can be used to expand to composites of more objects.
Said another way, in this system 700, multiple bucket detectors 720, 728, 736 are in the path of multiple objects 718, 726, 734 and illuminated by entangled photons from source 702. Generally, when detectors 720, 728, 736 all see a photon at the same time an image pixel is registered by a spatial sensitive detector 712. Other combinatorial logic behind the detectors 712, 720, 728, 736 can be used. For example, if AND conditions are met at D2720 and D1712, an image of a lightning bolt would be provided. If AND conditions are met at D3728 and D1712, an image of a cross would be provided. If AND conditions are met at D4736 and D1712, an image of a moon would be provided. All three pictures can be gathered by keeping all three of these pixel arrays in memory.
While the Applicant's teaching is described in conjunction with various embodiments, it is not intended that the applicant's teaching be limited to such embodiments. On the contrary, the Applicant's teaching encompasses various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art, which may be made therein without departing from the spirit and scope of the teaching.
