Patent Application
20160028541
There have been recent proposals for implementing the quantum cryptographic protocol BB92 with quantum states based on pulse-position modulation instead of polarization. Attempts to do so to date have been flawed; they are vulnerable to eavesdropping attacks since they do not fully implement the BB92 protocol. Some such approaches are detailed in Nazarathy, “Quantum key distribution over a fiber-optic channel by means of pulse position modulation,” Optics Letters 1533, 30 (2005).
What is needed is a quantum cryptographic protocol BB92 with quantum states based on pulse-position modulation which addresses these issues, and other issues that become apparent in the discussion below.
Embodiments are illustrated by way of example, and not by way of limitation, in figures of the accompanying drawings in which like reference numerals refer to similar elements.
In the following detailed description of example embodiments of the invention, reference is made to specific examples by way of drawings and illustrations. These examples are described in sufficient detail to enable those skilled in the art to practice the invention, and serve to illustrate how the invention may be applied to various purposes or embodiments. Other embodiments of the invention exist and are within the scope of the invention, and logical, mechanical, electrical, and other changes may be made without departing from the subject or scope of the present invention. Features or limitations of various embodiments of the invention described herein, however essential to the example embodiments in which they are incorporated, do not limit the invention as a whole, and any reference to the invention, its elements, operation, and application do not limit the invention as a whole but serve only to define these example embodiments. The following detailed description does not, therefore, limit the scope of the invention, which is defined only by the appended claims.
A system 100 for Quantum Key Distribution (QKD) via pulse position modulation is shown in
Quantum Key Distribution, when done properly, guarantees the secrecy of the distributed key. If an eavesdropper (Eve 110) tries to determine the key, she will introduce transmission errors in the distribution of the key and will be detected; the shared secret key can then be discarded before it is used to transmit compromised data. If, on the other hand, no eavesdropping is detected, the secrecy of the distributed key is guaranteed.
Pulse position modulation coding of bits 0 and 1 is illustrated in
As shown in
P|0>
P|1>
Bob publicly announces, at 206, the indices of those measurements (projections) in which he got a positive result (=1). Alice privately constructs the substring which consists of the bits she sent Bob with the same indices as those Bob just publicly announced. Alice reveals a portion of the substring at 208.
Bob privately constructs the string
for each index i he announced. Alice's substring and the string Bob constructs must be identical in the absence of noise and or eavesdropping. Public discussion follows as in the standard BB84 protocol. That is, a portionn of the raw common bits are publicly revealed at 208 and 210 and a check is made at 214 to make sure they are identical. If they are not, eavesdropping is concluded at 216 and the whole procedure is discarded. If they are, then the remaining unrevealed bits are used as the shared secret key at 218.
In the new PPM protocol, the state |0> is encoded as the state “pulse is in second bin” represented by |0>, |t2>, and the state |1> is encoded as the state “pulse is in coherent superposition of the first and second bins,” represented by |1>≡(|t1>+|t2>)/√{square root over (2)}. An example pulse position modulation encoder is shown in
The first key requirement is the efficient construction of the states:
|0>≡|t2> and |1>≡(|t1>+|t2>)/√{square root over (2)},
The construction of the state |0> is the same as the classical PPM state. The construction of the superposition state |1>, however, is more complex because, as noted above, |1>≡(|t1>+|t2>)/√{square root over (2)}. A pulse position modulation encoder for encoding |1>≡(|1>+|t2>)/√{square root over (2)} is shown in
The second key requirement is the construction of the projection operators P|0>
In the example embodiment shown in
In one example embodiment, the measurement P|0>
Likewise, the measurement P|1>
As noted above, precise clock synchronization is required between Alice 102 and Bob 104. In one example embodiment, this is achieved, at least in part, via an ultra-stable frequency reference such as described in U.S. patent application Ser. No. 13/400,348, filed by Wilkerson et al. on Feb. 20, 2012 the description of which is incorporated herein by reference. Synchronization of distant ultra-stable clocks can be achieved via a number of methods such as the Einstein synchronization protocol using optical two-way time transfer, with either optical fiber or free-space propagation.
In some embodiments, the ultra-stable frequency reference generating system described in U.S. patent application Ser. No. 13/400,348 includes a cavity-stabilized reference laser that includes a laser source locked to a stabilized cavity. In some such embodiments, the system also includes a Rubidium (Rb) cell that may be interrogated by a stabilized laser output of the cavity-stabilized reference laser to cause at least a two-photon Rubidium transition (to an upper state) within the Rubidium cell. A detector detects fluorescence within the Rubidium cell resulting from the spontaneous decay of the upper state Rubidium transition. Other vapor cell references can be used as well.
In vapor cell embodiments, the detector provides a detector output at a wavelength of the fluorescence to lock the cavity-stabilized reference laser to generate a stabilized laser output. In some such embodiments, the laser source is locking to both the stabilized cavity and to the Rubidium transition within the Rubidium cell. The combination of a cavity stabilized laser and femtosecond frequency comb referenced to the 778 nm two-photon transition in Rubidium as a source of ultra-low phase noise optical and microwave frequencies can be used, for instance, as standards in a compact system configuration.
As noted in the patent application, such systems are useful in systems that require synchronization; they are also suitable for use in, for instance, radar systems, communication systems, signal-collection systems and difficult EMI environments.
The description and the drawings herein sufficiently illustrate specific embodiments to enable those skilled in the art to practice them. Other embodiments may incorporate structural, logical, electrical, process, and other changes. Portions and features of some embodiments may be included in, or substituted for, those of other embodiments. Embodiments set forth in the claims encompass all available equivalents of those claims.
What have been described above are new systems and methods for quantum key distribution. The systems and methods described fully implement the BB92 protocol and which thus have the same absolute unconditional security properties as the standard polarization-based QKD protocol BB84. In one embodiment, a new method of encoding a |1> simplifies construction of a quantum key encoder.
Embodiments may be implemented in one or a combination of hardware, firmware and software. Embodiments may also be implemented as instructions stored on a computer-readable storage device, which may be read and executed by at least one processor to perform the operations described herein. A computer-readable storage device may include any non-transitory mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a computer-readable storage device may include read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash-memory devices, and other storage devices and media. In some embodiments, the system may include one or more processors and may be configured with instructions stored on a computer-readable storage device.
