Abstract:
Methods and apparatus for generating coherent optical pulses (P 1′ , P 2′ ) in a quantum key distribution (QKD) station (Alice-N) of a QKD system ( 10 ) without using an optical fiber interferometer ( 12 ) are disclosed. The method includes generating a continuous wave (CW) beam of coherent radiation (R) having a coherence length LC and modulating the CW beam within the coherence length. The invention obviates the need for an interferometer loop to form multiple optical pulses from a single optical pulse, thereby obviating the need for thermal stabilization of the interferometer loop at the QKD station Alice-N.

Description:
CLAIM OF PRIORITY 
       [0001]    This application claims the benefit of priority under 35 U.S.C. § 119(e) of U.S. Provisional Application Ser. No. 60/608,782, filed on Sep. 10, 2004. 
     
    
     TECHNICAL FIELD OF THE INVENTION 
       [0002]    The present invention relates to quantum cryptography, and in particular relates to and has industrial utility in connection with a one-way quantum key distribution (QKD) system. 
       BACKGROUND OF THE INVENTION 
       [0003]    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 and reveal her presence. 
         [0004]    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 publications by C. H. Bennett et al entitled “Experimental Quantum Cryptography” and by C. H. Bennett entitled “Quantum Cryptography Using Any Two Non-Orthogonal States”, Phys. Rev. Lett. 68 3121 (1992). 
         [0005]    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. 
         [0006]    The above mentioned publications by Bennett each describe a QKD system wherein Alice randomly encodes the polarization or phase of single photons at one end of the system, and Bob randomly measures the polarization or phase of the photons at the other end of the system. The QKD system described in the Bennett 1992 paper is based on two optical fiber Mach-Zehnder interferometers (one at Alice and one at Bob). Respective parts of the interferometric system are accessible by Alice and Bob so that each can control the phase of the interferometer. 
         [0007]      FIG. 1  is a schematic diagram of a prior art QKD system  10  based on those disclosed in U.S. Pat. No. 5,307,410 to Bennett (“the Bennett patent”) and U.S. Pat. No. 5,953,421 to Townsend (“The Townsend patent), which patents are incorporated herein by reference. QKD system  10  includes two QKD stations Bob and Alice. Not shown in  FIG. 1  are controllers in Alice and Bob that control the operation of their respective elements, and that are in operable communication with each another to coordinate the operation of the QKD system as a whole. 
         [0008]    Alice includes a laser source L 1  and a first interferometer loop  12  with arms  14  and  16  that have different lengths. One of the interferometer arms (say,  14 ) includes a modulator (polarization or phase) M 1 . Interferometer loop  12  is coupled to an optical fiber link FL, which is connected to a second interferometer loop  22  at Bob. Loop  22  includes arms  24  and  26  of different lengths with a phase modulator M 2  in one of the arms (say arm  24 ). Loop  22  is coupled to a detector unit  30  via an optical fiber section F 3 . The detector unit  30  may include, for example, two single-photon detectors (SPDs) coupled to optical fiber section F 3  by an optical coupler, such as illustrated and discussed in the Townsend patent. Detector unit  30  may also include a single SPD, such as illustrated and discussed in the Bennett patent. 
         [0009]    In operation, laser source L 1  generates a light pulse P 0  that is divided into two pulses P 1  and P 2  by first interferometer loop  12 . One of the pulses (say P 1 ) travels over arm  14  and is randomly modulated polarization- or phase-modulated by modulator M 1 . The two pulses, which are now separated due to the different path lengths of the interferometer arms, are attenuated to so that they are weak (i.e., one or less photons per pulse on average). The photons then travel over fiber link FL to second interferometer loop  22 . 
         [0010]    At interferometer  22 , each pulse P 1  and P 2  is then split into two pulses (P 1  into P 1   a  and P 1   b  and P 2  into P 2   a  and P 2   b ). Two of the pulses (say P 1   a  and P 2   a ) travel over arm  24 , while the other two pulses (say P 1   b  and P 2   b ) travel over arm  26 . One of these pulses (say, P 2   a ) travels over arm  24  is randomly modulated by modulator M 2 . 
         [0011]    The second interferometer loop then combines the pulses onto fiber section F 3 . If the two interferometer loops have the same path length (e.g., the lengths of arms  14  and  24  are the same and the lengths of arms  16  and  26  are the same), then the two pulses that travel the same optical path length (say, pulses P 2   a  and P 2   b ) interfere to create a single interfered pulse I. The other pulses enter fiber section F 3  separated from one another because they followed optical paths of different lengths. 
         [0012]    The interfered pulse I is then detected by detector unit  30  in a manner that reflects the phase or polarization imparted to the interfered pulse by modulators M 1  and M 2 . The process is repeated to create a number of interfered pulses  1 , which are detected and processed according to known QKD techniques to establish a secret key between Alice and Bob. 
         [0013]    The use of an interferometer loop formed from optical fibers or beam splitters to create multiple pulses is standard in QKD systems. However, such arrangements tend to be lossy and are fairly complex because the loops have to be thermally stabilized. Further, there is a strict requirement for interferometer arm balancing. A laser LS 1  normally has narrow pulses (for example, with full width at half maximum (FWHM) of approximately 100 ps), so the lengths of short-long arms should be balanced within an accuracy of hundreds of microns to obtain a good extinction ratio. Interfering pulses (e.g. P 2   a  and P 2   b ) should overlap in the time domain. In manufacturing, this puts strict requirements on fiber splicing and system component selection. 
         [0014]    In addition, in a commercially viable QKD system, the interferometers at Alice and Bob should be manufactured together so that they are matched. This also puts limitations on practical system deployment and maintenance: if either the Alice or the Bob interferometer needs to be replaced, the other one needs to be replaced as well with a matching interferometer. Accordingly, it would be desirable to have another way to create the multiple coherent pulses at Alice with less loss and in a simpler manner that, for example, obviates the need for stabilizing one of the interferometers and the need for matching interferometers in the system. 
       DESCRIPTION OF THE INVENTION 
       [0015]    One aspect of the invention is a method of generating two or more coherent optical pulses in a first station of a QKD system. The method includes generating a continuous wave (CW) beam of coherent radiation having a coherence length LC and modulating the CW beam within the coherence length LC so as to create two or more coherent optical pulses of radiation. The method also includes sending the two or more coherent optical pulses as weak pulses to a second QKD station optically coupled to the first QKD station. 
         [0016]    Another aspect of the invention is a QKD station of a QKD system. The QKD station includes a laser source adapted to emit a continuous wave (CW) beam of radiation having a coherence length LC. The station also includes a first modulator optically coupled to the laser source and adapted to modulate the radiation beam within the coherence length LC to create two or more coherent optical pulses. The station further includes a second modulator downstream of the first modulator and optically coupled thereto, the second modulator adapted to modulate at least one of the two or more coherent optical pulses. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  is a schematic diagram of a prior art QKD system; and 
           [0018]      FIG. 2  is a schematic diagram of the pulse generation unit of the present invention as part of Alice in the QKD system illustrated in  FIG. 1 . 
           [0019]      FIG. 3  is a schematic diagram of the pulse detection unit as part of Bob in the QKD system with Alice as illustrated in  FIG. 2 ; and 
           [0020]      FIG. 4  is an alternative embodiment of the pulse detection unit as part of Bob in the QKD system with Alice 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 BEST MODE OF THE INVENTION 
       [0022]    The present invention relates to quantum cryptography, and in particular relates to and has industrial utility in connection with quantum key distribution (QKD) systems. 
       New Alice 
       [0023]      FIG. 2  is a close-up schematic diagram of a new Alice—called Alice N—for the QKD system of  FIG. 1 , wherein the interferometer loop  12  is replaced with an optical pulse generator  100 . Optical Pulse generator  100  includes a laser source LS 2  optically coupled (e.g., via an optical fiber section F 1 ) to an intensity modulator M 3 . Modulator M 1  is optically coupled (e.g., via optical fiber section F 2 ) to and is downstream of modulator M 3 . 
       The Laser Source 
       [0024]    In an example embodiment, laser source LS 2  is a continuous-wave (CW) laser that emits radiation R. In an example embodiment, laser source LS 2  is a CW laser with coherence length complying with the requirements presented below. In an example embodiment, laser source LS 2  has a coherence length LC on the order of nanoseconds (ns), e.g., in the range from about 1 ns to about 100 ns. Laser source LS 2  may be, for example, a solid-state laser, such as an external-cavity diode laser. 
         [0025]    There are other important requirements for the laser source coherence length and laser source frequency stabilization. To obtain interference, pulses P 1 ′ and P 2 ′ (discussed below) should be separated by a distance smaller than the laser source coherence length. The CW laser source LS 2  should be frequency stabilized and have a narrow line width. 
         [0026]    If Bob&#39;s interferometer  22  has a fiber length difference (for two arms) of ΔL, the phase difference Δφ between signals of two different frequencies is 
         [0000]      Δφ=(2 π/c )(Δ L )(Δ f )  (EQ. 1) 
         [0000]    where c is the speed of light, and Δf is the difference between two frequencies. The difference in frequencies of the signals can arise, for example, from the laser source LS 2  changing its output frequency because it is not properly frequency stabilized. 
         [0027]    One can estimate the frequency stabilization requirements from EQ. 1, above. For example, for ΔL=1 m, and if from an interference extinction ratio phase difference is required to be about 1°, the laser frequency stability requirement is about 
         [0000]      Δf&lt;1 MHz.  (EQ. 2) 
       The Intensity Modulator 
       [0028]    Also in an example embodiment, modulator M 3  is a lithium niobate (LiNbO 3 ) modulator capable of rapidly switching on and off on a time scale on the order of tens to hundreds of picoseconds (ps). In another example embodiment, modulator M 3  is an electro-absorption modulator. Modulator M 3  preferably has a high extinction ratio so that it can create sharp optical pulses, as described below. 
         [0029]    Modulator M 3  is coupled to a controller  50 A. Controller  50 A is also coupled to laser source LS 2  and to modulator M 1 . Alice-N also typically includes a variable optical attenuator (VOA)  52  coupled to the controller to ensure that pulses leaving Alice are weak (i.e., one photon or less on average). Controller  50 A also acts to stabilize the frequency of laser source LS 2 . In addition, controller  50 A is operably coupled to a controller  50 B at Bob ( FIGS. 3 and 4 ) so that the operation of the system as a whole is properly coordinated. 
       Operation of the QKD System with the Alice-N 
       [0030]    With continuing reference to  FIG. 2 , in operation controller  50 A activates laser source LS 2  via an activation signal S 2 . In response, laser source LS 2  generates continuous laser radiation R. Laser radiation R is shown as a section of a CW beam, wherein the section has a coherence length LC. 
         [0031]    Controller  50 A sends a modulation signal S 3  to modulator M 3  to modulate radiation R. Modulator M 3  modulates radiation R with sufficient speed (e.g., within the coherence length LC) and extinction to create two or more sharp, coherent radiation pulses. Two such pulses P 1 ′ and P 2 ′ are shown and discussed below for the sake of illustration. 
         [0032]    In an example embodiment, pulses P 1 ′ and P 2 ′ have pulse widths ranging anywhere from 20 to 100 ps and are separated by intervals ranging from about 1 ns to 100 ns. Note that if arms  24  and  26  of Bob&#39;s interferometer differ in length by 10 cm, the corresponding pulse separation is 0.5 ns. Generally, the width and spacing of the pulses formed by modulator M 3  are dictated by the gating pulse width of detector unit  30  and the requirement that the non-interfering pulses not overlap after leaving Bob&#39;s interferometer loop  22   
         [0033]    Pulses P 1 ′ and P 2 ′ proceed to (phase) modulator M 1 , whose timing is coordinated with the operation of modulator M 3  via signal S 1  from controller  50 A, so that modulator M 1  selectively randomly modulates at least one of pulses P 1 ′ and P 2 ′. The two pulses are then attenuated by VOA  52  via an attenuation signal SA from controller  50 A (if necessary). The pulses then proceed onto optical fiber link FL and travel over to Bob, where they are processed according to known QKD techniques. In an example embodiment, the one or more pulses formed in this manner constitute a quantum signal SQ. 
         [0034]    From Bob&#39;s point of view, it is as if pulses P 1 ′ and P 2 ′ were created in the usual manner using an interferometer loop or the like. However, the advantage of using optical pulse generator  100  is that Alice-N no longer needs to be thermally stabilized to the high degree required for interferometer loops. This greatly reduces the cost and complexity of fabricating and maintaining a QKD system in working condition for long periods of time. 
       New Bob 
       [0035]    The present invention allows for new designs for Bob, referred as Bob-N.  FIG. 3  is a schematic diagram of an example embodiment of Bob-N suitable for use with Alice-N of  FIG. 2 . In Bob-N of  FIG. 3 , elements  27  and  29  are each light splitting/combining elements, such as a coupler or a  50 - 50  beamsplitter. Also shown is Bob-N&#39;s controller  50 B operably coupled to modulator M 2  and to Alice-N&#39;s controller  50 A. 
         [0036]    In operation, after pulses P 1 ′ a , P 1 ′ b , P 2 ′ a  and P 2 ′ b  interfere at coupler  29 , three pulses result: S 1 , I and S 2 , where the interfered pulse I is the result of the interference of pulses which followed the short-long and long-short paths. Interfered pulse I carries the modulation (phase) coding information from modulators M 1  and M 2 . Optical side-pulses S 1  and S 2  are separated from the interfered central pulse I to avoid pulse overlapping during gating of detector unit  30 . For example, if a gating pulse has a width of 2 ns, side peaks S 1  and S 2  should be a few nanoseconds away from each other. This dictates the tolerance on Bob&#39;s interferometer, i.e., the allowable mismatch in the optical path of arms  24  and  26  (approximately 5 ns pulse separation corresponds to 1 m). 
         [0037]      FIG. 4  is a schematic diagram of another example embodiment Bob-N suitable for use with Alice-N as illustrated in  FIG. 2  In Bob-N of  FIG. 4 , element  28  is a fast optical switch that is fast enough to switch between pulses P 1 ′ and P 2 ′. The first incoming pulse is routed to a longer arm of interferometer and the second incoming pulse is routed to the shorter arm. After pulses P 1 ′ and P 2 ′ interfere at element  29 , only one interference peak (signal) I appears. The advantage of using optical switch for element  28  is that Bob&#39;s interferometer arm length difference can be made very small, e.g., small enough for an integrated waveguide form design for the interferometer  22 . This simplifies interferometer stabilization (e.g., for thermal and mechanical drifts) and laser frequency stabilization at Bob-N. 
       Example Interferometer Balancing Method 
       [0038]    The present invention includes methods for balancing arms  24  and  26  of interferometer  22 . The method includes generating the optical pulses P 1 ′ and P 2 ′ at Alice-N as discussed in detail above and sending them to interferometer  22  at Bob-N. The method then includes measuring the interference of pulses exiting interferometer  22 , e.g., the interference between pulses P 2 ′ a  and P 2 ′ b  at detector unit  30 . The method further includes adjusting the modulation of the CW radiation R, and optionally adjusting the delay between two pulses, as well as the pulse amplitudes, based on the measurement at detector unit  30 . This is done in order to obtain a desired measurement at detector unit  30 , or a desired interference at the output of interferometer  22 . This feedback technique is made possible by the operable connection between controllers  50 A and  50 B of Alice-N and Bob-N, respectively. 
         [0039]    A QKD system based on present invention preferably employs a form of polarization control at Bob&#39;s interferometer  22  (i.e., after fiber propagation), such as shown in Townsend patent. Also in an example embodiment, Bob&#39;s interferometer is thermally stabilized with a feed-back loop. An example of a thermal stabilization feedback loop for a QKD system is described in U.S. patent application Ser. No. 10/882,013, entitled “Temperature compensation for QKD systems,” which patent application is incorporated by reference herein.