Abstract:
Systems and methods for suppressing the unwanted detection of backscattered light in a two-way quantum key distribution (QKD) system is disclosed. The system includes a first QKD station that has two or more laser sources that emit light at different wavelengths, and corresponding two or more sets of detectors. In a two-way QKD system, backscattered light is typically generated in an optical fiber link connecting the first and second QKD stations by the relatively strong outgoing optical pulses. To prevent the backscattered light from interfering with the detection of the weak optical pulses returned from the second QKD station to the first station, a controller sequentially activates different light sources, and also sequentially activates the different sets of detectors.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to quantum cryptography, and in particular relates to quantum key distribution (QKD) systems, and more particularly to two-way QKD systems.  
       BACKGROUND OF THE INVENTION  
       [0002]     Quantum key distribution involves establishing a key between a sender (“Alice”) and a receiver (“Bob”) by using weak (e.g., 0.1 photon on average) optical signals transmitted over a “quantum channel.” The security of the key distribution is based on the quantum mechanical principle that any measurement of a quantum system in unknown state will modify its state. As a consequence, an eavesdropper (“Eve”) that attempts to intercept or otherwise measure the quantum signal will introduce errors into the transmitted signals, thereby revealing her presence.  
         [0003]     The general principles of quantum cryptography were first set forth by Bennett and Brassard in their article “Quantum Cryptography: Public key distribution and coin tossing,” Proceedings of the International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984, pp. 175-179 (IEEE, New York, 1984). Specific QKD systems are described in U.S. Pat. No. 5,307,410 to Bennett, and in the article by C. H. Bennett entitled “Quantum Cryptography Using Any Two Non-Orthogonal States”, Phys. Rev. Lett. 68 3121 (1992).  
         [0004]     The general process for performing QKD is described in the book by Bouwmeester et al., “The Physics of Quantum Information,” Springer-Verlag 2001, in Section 2.3, pages 27-33. During the QKD process, Alice uses a random number generator (RNG) to generate a random bit for the basis (“basis bit”) and a random bit for the key (“key bit”) to create a qubit (e.g., using polarization or phase encoding) and sends this qubit to Bob.  
         [0005]     The article by Ribordy et al., entitled “Automated ‘Plug and play” quantum key distribution,” Electronics Letters Vol. 34, No. 22 Oct. 29, 1998 (“the Ribordy paper”) and the U.S. Pat. No. 6,188,768 each describe a so-called “two way” system wherein quantum signals are sent from a first QKD station to a second QKD station and then back to the first QKD station. Typically, the quantum signals sent from the first QKD station to the second QKD station are relatively strong (e.g., hundreds or thousands of photons per pulse on average), and are attenuated down to quantum levels (i.e., one photon per pulse or fewer) at the second QKD station prior to being returned to the first QKD station.  
         [0006]     The performance of a two-way QKD system is degraded by noise in the form of photons generated from the initially relatively strong quantum signal by three different mechanisms: 1) forward Raman scattering, in which frequency-shifted photons are generated and co-propagate with the quantum signal photons; 2) Raman backscattering, in which frequency-shifted photons are generated and propagate in the opposite direction to the quantum signal photons; and 3) Rayleigh scattering, in which photons from the quantum signal are elastically scattered back in the opposite direction of the quantum signal photons.  
         [0007]     It is possible to minimize noise from Raman forward scattering and backscattering by wavelength-division multiplexing (WDM), time-division multiplexing (TDM) or wavelength filtering. However, Rayleigh backscattering presents a more difficult problem because Rayleigh backscattered photons have the same frequency as the quantum signal photons. Thus, WDM solutions that attempt to separate quantum signals from the noise they generate are not applicable. In addition, since the Rayleigh backscattered photons are elastically scattered throughout the transmission fiber, they arrive at the detectors at a constant (continuous wave) rate, making TDM solutions ineffective.  
         [0008]     It is important to note that the two-way QKD system described in the Ribordy paper uses a “storage line” in the form of a 13.2 km long fiber loop to suppress the detection of Rayleigh backscattered light. Such a storage line adversely affects the transmission rate of a two-way QKD system.  
       SUMMARY OF THE INVENTION  
       [0009]     One aspect of the invention is a QKD station adapted for optical coupling via an optical fiber to a second QKD station of a QKD system. The QKD station includes first and second laser sources each adapted to emit outgoing optical pulses into the optical fiber. The outgoing optical pulses have first and second wavelengths corresponding to that of the first and second laser sources. The QKD station also includes first and second single-photon detectors (SPDs) respectively adapted to detect optical pulses of the first and second wavelengths as incoming weak optical pulses returned to the first QKD station from another QKD station. In an example embodiment, the SPDs are arranged as pairs, where each pair detects a given wavelength. Also included in the QKD station is a controller operably coupled to the first and second laser sources and to the first and second SPDs. The controller is adapted to sequentially activate and deactivate the first and second laser sources to generate corresponding first and second sets of the outgoing optical pulses. The controller is additionally adapted to sequentially activate and deactivate the first and second SPDs to reduce an amount of backscattered light formed in the optical fiber by the outgoing pulses from being detected by the first and second SPDs.  
         [0010]     Another aspect of the invention is a method of detecting optical pulses in a QKD system having first and second QKD stations. The method includes transmitting a first set of optical pulses having a first wavelength from a first QKD station to a second QKD station, terminating the transmission of the first set of optical pulses, and transmitting a second set of optical pulses having a second wavelength from the first QKD station to the second QKD station at a time that prevents backscattered radiation from the first set of optical pulses from being detected in the first QKD station.  
         [0011]     Another aspect of the invention is a method of reducing Rayleigh backscattering in a QKD system having first and second QKD stations optically coupled via an optical fiber link. The first QKD station has first and second selectively activatable single-photon detectors (SPDs) optically coupled to the optical fiber link and adapted to detect single photons having respective first and second wavelengths. In an example embodiment, the SPDs are arranged in pairs, where each pair is adapted to detect a single wavelength. The method includes multiplexing in the first QKD station first and second sets of pairs of optical pulses into the optical fiber link. The first and second sets have the first and second wavelengths, respectively. The method also includes selectively activating the first and second SPDs to reduce or prevent backscattered light formed in the optical fiber link from being detected by the SPDs when detecting single photons. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  is a schematic diagram of an example two-way QKD system;  
         [0013]      FIG. 2  is a schematic diagram of an example embodiment of the QKD station Bob according to the present invention for use in the two-way QKD system of  FIG. 1 , wherein Bob is capable of transmitting quantum signals having three different wavelengths;  
         [0014]      FIG. 3A  is a schematic diagram that illustrates the timing of generating optical pulses of a second wavelength when optical pulses of a first wavelength are arriving at their corresponding single-photon detectors (SPDs);  
         [0015]      FIG. 3B  is a schematic diagram that illustrates the timing of generating optical pulses of a third wavelength when optical pulses of the second wavelength are arriving at their corresponding SPDs;  
         [0016]      FIG. 4  is a timing diagram illustrating the time segments over which the laser sources send their respective optical pulses of different wavelengths;  
         [0017]      FIG. 5A  is a schematic diagram that illustrates the timing of generating optical pulses of a second wavelength when optical pulses of a first wavelength are arriving at their corresponding single-photon detectors (SPDs);  
         [0018]      FIG. 5B  is a schematic diagram that illustrates the timing of generating optical pulses of a third wavelength when optical pulses of the second wavelength are arriving at their corresponding SPDs;  
         [0019]      FIG. 6  is a schematic diagram of a portion of Bob illustrating the use of a multiplexer instead of three separate optical couplers; and  
         [0020]      FIG. 7  is a schematic diagram of a portion of Bob illustrating the use of a single polarization-maintaining variable optical attenuator (PM VOA) arranged downstream of the multiplexer, instead of using three separate PM VOAs as illustrated in  FIG. 2 . 
     
    
       [0021]     The various elements depicted in the drawings are merely representational and are not necessarily drawn to scale. Certain sections thereof may be exaggerated, while others may be minimized. The drawings are intended to illustrate various embodiments of the invention that can be understood and appropriately carried out by those of ordinary skill in the art.  
       DETAILED DESCRIPTION OF THE INVENTION  
       [0022]     The present invention relates to a two-way QKD system, and in particular to a method of suppressing noise in such a QKD system that arises from Rayleigh backscattering.  FIG. 1  is a schematic diagram of an example two-way QKD system  10 . QKD system  10  includes a first QKD station “Bob” and a second QKD station “Alice” connected to each other via an optical fiber link FL. Optical signals (pulses) P are sent over optical fiber link FL between Alice and Bob. These optical pulses are also referred to herein as “quantum pulses” because they are sent over what is referred to in the art as the “quantum channel.” 
         [0023]     The optical (quantum) pulses returned from Alice to Bob, as described below, generally have an average number of photons of 1 or fewer, and preferably about 0.1. The details of Bob according to the present invention are below.  
         [0024]     With continuing reference to  FIG. 1 , in an example embodiment, Alice includes a variable optical attenuator (VOA)  12 , a phase modulator  14  and a Faraday mirror  16  arranged in order along an optical axis A 1 . Alice also includes a controller  20  coupled to VOA and to phase modulator  14  to control the operation of these elements.  
         [0025]     In an example embodiment, Alice and Bob are also coupled via a synchronization channel SC that allows for synchronization signals SS to be sent from one station to the other to control the timing and operation of the various elements making up the QKD system. In an example embodiment, the synchronization channel SC is multiplexed with the quantum channel over optical fiber link FL.  
         [0026]     Bob  FIG. 2  is a schematic diagram of an example embodiment of Bob according to the present invention suitable for use in the two-way QKD system  10  of  FIG. 1 . Bob includes a plurality of laser sources L—for example three laser sources L 1 , L 2  and L 3 , as shown. Lasers L 1 , L 2  and L 3  emit respective optical pulses P 1 , P 2  and P 3  having respective wavelengths λ 1 , λ 2 , and λ 3 .  
         [0027]     Lasers L 1 , L 2  and L 3  are optically coupled to respective polarization-maintaining (PM) VOAs  51 ,  52  and  53  e.g., via respective fiber sections F 1 , F 2  and F 3 . PM VOAs  51 ,  52  and  53  are in turn optically coupled to respective couplers  61 ,  62  and  63  e.g., via fiber sections F 4 , F 5  and F 6 . Couplers  61 ,  62  and  63  are arranged in series, with coupler  63  optically coupled to coupler  62 , e.g., via fiber section F 7 , and coupler  62  optically coupled to coupler  61 , e.g., via fiber section F 8 . Lasers L 1 , L 2  and L 3 , and PM VOAs  51 ,  52  and  53  are operably (e.g., electrically) coupled via a (branching) line  64  (e.g., a wire) to a controller  66  that controls the activation and timing of these elements, as discussed in detail below.  
         [0028]     Bob further includes a circulator  70  with ports  70 A,  70 B and  70 C. Coupler  61  is optically coupled to first circulator port  70 A, e.g., via a fiber section F 9 . Also, a 3 dB coupler  80  with four ports  80 A- 80 D is optically coupled to third circulator port  70 C, e.g., via a fiber section F 10  connected to the coupler at port  80 A.  
         [0029]     Coupler  80  is coupled to two fiber sections  82  and  84  at respective ports  80 D and  80 C. The opposite ends of fibers  82  and  84  are coupled to respective faces  88 A and  88 B of a polarizing beam splitter  88 , thereby forming an interferometer loop  100  with arms  82  and  84 . A phase modulator  110  is arranged in one of the arms (e.g., arm  82 ). Phase modulator  110  is operatively coupled to controller  66 .  
         [0030]     Bob also includes a first WDM demultiplexer  120  optically coupled to port  70 B of circulator  70  and a second WDM demultiplexer  122  optically coupled to coupler  80  at port  80 B. First demultiplexer  120  is optically coupled to a detector unit  128  having three single-photon detectors (SPDs)  130 ,  132  and  134  (e.g., via respective optical fibers  136 ). Second demultiplexer  122  is optically coupled to a detector unit  138  having three single-photon detectors  140 ,  142  and  144  (e.g., via respective optical fibers  146 ). Each of the single-photon detectors is in turn coupled to controller  66 . SPDs  130  and  140  corresponding to laser source L 1  and λ 1 , SPDs  132  and  142  correspond to laser source L 2  and λ 2 , and SPDs  134  and  144  correspond to laser source L 3  and λ 3 . The SPD pairs constitute a set of SPDs that correspond to each wavelength used.  
         [0031]     Note that the above description is an example embodiment of an arrangement for Bob. Other arrangements are possible, and the above-described arrangement is for the sake of illustration. For example, rather than SPD pairs, Bob can operate using a single SPD for each wavelength of light, e.g., by means of a delay line and gating pulses provided by controller  66 . The discussion below uses SPD pairs for ease of illustration and understanding.  
         [0000]     Method of Operation  
         [0032]     In the present invention, both time and wavelength demultiplexing can be used to suppress the adverse effects associated with Rayleigh backscattering. Generally, backscattering occurs over the length of the optical fiber and backscattered light can reach the SPDs from portions of the optical fiber as far as at or near Alice. In certain instances, however, most of the backscattering in QKD system  10  ( FIG. 1 ) occurs in the portions of optical fiber link FL near Bob where the original outgoing optical pulses P are still strong. These pulses also have a higher probability of reaching a detector since they are less likely to be lost in fiber link FL on the way back to Bob. Generally, there is some effective distance along the length of the fiber link FL as measured from Bob beyond which the effects of backscattering on the detection process are minimal. In an example embodiment, this effective distance is determined empirically by varying the timing of the generation and detection of optical pulses of different wavelength to find an optimal timing arrangement.  
         [0033]     With continuing reference to  FIG. 2 , to minimize the adverse effects of Rayleigh backscattering, laser sources L 1 , L 2  and L 3  and the corresponding SPDs are operated in sequence. For example, laser source L 1  generates a number (set) N 1  of pulses P 1  that pass through PM VOA  51 , through coupler  61 , through circulator  70 , and to loop  100 . At loop  100 , each pulse P 1  is split into two coherent optical pulses, shown generically in  FIG. 2  as Pn′ and Pn″. The pairs of pulses travel to Alice where at least one pulse in each pair is modulated. The pulse pairs are then returned to Bob where the returned pulses that travel through arm  82  are phase modulated with a randomly selected phase (e.g., via a random number generator in controller  66 ).  
         [0034]     Each returned pair of pulses is recombined (interfered) at coupler  80  to form a single interfered pulse IP 1  (see  FIG. 3A ). The interfered pulse passes either to demultiplexer  122  via coupler  80  or to demultiplexer  120  through circulator  70 , depending on the overall phase of the interfered pulse. Demultiplexer  120  or  122  then directs the interfered pulse (which has a wavelength λ 1 ) to SPD  130  or  140  in respective detector units  128  and  138 . The operation of SPD  130  and  140  is gated via controller  66  to correspond to the arrival time of the interfered pulse  
         [0000]     Backscattering Along The Entire Fiber Length  
         [0035]     In the most general case, backscattering in QKD system  10  ( FIG. 1 ) occurs along the entire length of optical fiber link FL.  
         [0036]     With reference also to  FIG. 3A , at or about the time when the first set of optical pulses arrives at Alice, controller  66  deactivates laser source L 1  and activates laser source L 2 . Laser source L 2  then emits a number (set) N 2  of optical pulses P 2 . Optical pulses P 2  pass through PM VOA  52 , through coupler  62  and pass to coupler  61 . Likewise, with reference to  FIG. 3B , at or about the time when optical pulses P 2  start arriving at Alice (and at or about the time when interfered pulses IP 1  are formed in Bob), controller  66  deactivates laser source L 2  and activates laser source L 3 , which emits a number (set) N 3  of optical pulse P 3 . Then, at or about the time when optical pulses P 3  start arriving at Alice, controller  66  deactivates laser source L 3  and activates laser source L 1  and the process repeated.  
         [0037]     In the meantime, controller  66  sequentially activates SPD pairs  130  and  140 ,  132  and  142 , and  134  and  144  to detect respective interfered optical pulses IP 1 , IP 2  and IP 3  having respective wavelengths λ 1 , λ 2  and λ 3  as the different optical pulse sets sequentially arrive at Bob.  
         [0038]     Switching the wavelength of optical pulses P from one wavelength to another wavelength just as the optical pulses of one wavelength arrive at Alice prevents Rayleigh backscattered light of the one wavelength from reaching the SPDs designated to detect photons of that wavelength just as the quantum pulses of that wavelength are being detected.  
         [0039]     With reference to  FIG. 4 , in an example embodiment, each laser source L 1 , L 2  and L 3  emits sets of optical pulses for a time duration of L/C, and is off for the consecutive period of 2(LF)/c, where LF is the length of optical fiber link FL between Bob and Alice and c is the speed of light in the fiber. In a more general example embodiment where there are n laser sources L 1 , L 2 , . . . Ln, each laser emits for a time duration of LF/C and is off for the consecutive period of (n−1)(LF)/c. In this example embodiment, Rayleigh scattering is completely time-demultiplexed.  
         [0000]     Strongest Backscattering Near Bob  
         [0040]     As mentioned above, in certain instances, most of the backscattering in QKD system  10  ( FIG. 1 ) occurs in the portions of optical fiber link FL near Bob where the original outgoing optical pulses P are still strong. These pulses also have a higher probability of reaching a detector since they are less likely to be lost in fiber link FL on the way back to Bob.  
         [0041]     Accordingly, with reference also to  FIG. 5A , in one example embodiment, at or about the time when interfered pulses (photons) IP 1  start arriving at SPDs  130  and  140 , controller  66  deactivates laser source L 1  and activates laser source L 2 . Laser source L 2  then emits a number (set) N 2  of optical pulses P 2 . Optical pulses P 2  pass through PM VOA  52 , through coupler  62  and pass to coupler  61 . At this point, the operation of the QKD system is essentially the same as described above in connection with optical pulses P 1 , except that now SPDs  132  and  142  are gated to detect arriving interfered pulses having wavelength λ 2 .  
         [0042]     Likewise, with reference to  FIG. 5B , at or about the time when interfered pulses IP 2  having wavelength λ 2  start arriving at SPDs  132  and  142 , controller  66  deactivates laser source L 2  and activates laser source L 3 . Laser source L 2  then emits a number (set) N 3  of optical pulses P 3 . Optical pulses P 3  pass through PM VOA  53  and through couplers  63 ,  62  and  61 . At this point, the operation of the QKD system is essentially the same as described above in connection with optical pulses P 1 , except that now SPDs  134  and  144  are gated to detect arriving interfered pulses having wavelength λ 3 .  
         [0043]     At or about the time when interfered pulses IP 3  (not shown) start arriving at SPDs  134  and  144 , controller  66  deactivates laser source L 3  and activates. laser source L 1 , and the above-described process repeated until a desired number of qubits are exchanged. Generally, each laser source L 1 , L 2  . . . Ln emits for a time duration of 2(LF)/c and is off for the consecutive period of 2(n−1)(LF)/c.  
         [0044]     Switching the wavelength of optical pulses P from a first wavelength to a second wavelength just as the optical pulses of the first wavelength are being detected decreases the amount of Rayleigh backscattered light of the first wavelength from reaching the SPDs designated to detect photons of the first wavelength just as the quantum pulses of that wavelength are being detected. The amount of the decrease is non-uniform and increases exponentially with time during each cycle.  
         [0045]     The amount of Rayleigh backscattered photons, R, of a certain wavelength reaching the SPDs as this wavelength is being detected can be expressed as R=Ae −Bt , where time t varies between 0 and 2(LF)/C during each cycle, and where A and B are the system parameters that depend on fiber length (FL), its loss and the system architecture.  
         [0000]     Key Generation  
         [0046]     In the present invention, the conventional QKD protocols are used to extract a key from the exchanged optical pulses. When photons (pulses) are detected (i.e., as detector clicks) in the SPDs, it is important to know which SPD pair generated the click. When a detection event occurs in an SPD set that is not presently activated (gated), this event (click) should be discarded, since it corresponds to the wrong wavelength—and thus can be considered to originate from dark current or another type of detector error.  
         [0000]     Other Example Embodiment of Bob  
         [0047]      FIG. 6  is a schematic diagram of a section of Bob similar to that of  FIG. 2 , illustrating an example embodiment wherein a multiplexer  300  (e.g., a conventional optical multiplexer, a micro-electro-mechanical (MEMS) device, etc.) is used to combine the optical pulses P from the different laser sources L and send them to circulator  70 . This example embodiment eliminates the need for individual couplers  61 ,  62  and  63 .  
         [0048]      FIG. 7  is a schematic diagram of a section of Bob similar to that of  FIG. 5 , illustrating an example embodiment wherein a single PM VOA  310  is arranged downstream of multiplexer  300 . This example embodiment eliminates the need for three different PM VOAs.  
         [0049]     There are many other variations and example embodiments that could be set forth to describe the present invention. For example, the SPDs need not be arranged in pairs as described above, but may be arranged as single SPDs for each wavelength. Accordingly, the many features and advantages of the present invention are apparent from the detailed specification, and, thus, it is intended by the appended claims to cover all such features and advantages of the described apparatus that follow the true spirit and scope of the invention. In the foregoing Detailed Description, various features are grouped together in various example embodiments for ease of understanding. Furthermore, since numerous modifications and changes will readily occur to those of skill in the art, it is not desired to limit the invention to the exact construction, operation and example embodiments described herein.