Abstract:
Methods for calibrating the modulators in a QKD system ( 100 ) are disclosed. The methods include setting the voltage (V B ) of Bob&#39;s modulator (MB) to a positive value and then adjusting the voltage (V A ) of Alice&#39;s modulator (MA) in both the positive and negative direction to obtain overall relative phase modulations that result in maximum and minimum photon counts (N) in the two single-photon detectors ( 32   a   , 32   b ). Bob&#39;s modulator voltage is then set to a negative value and the process repeated. When the basis voltages (V B ( 1 ), V B ( 2 ), V A ( 1 ), V A ( 2 ), V A ( 3 ) and V A ( 4 )) are established, the QKD system is operated with intentionally selected incorrect bases at Bob and Alice to assess orthogonality of the basis voltages by assessing whether or not the probability of photon detection at the detectors is 50:50. If not, the modulator voltages are adjusted to be orthogonal. This involves changing Bob&#39;s basis voltage (V B ( 1 ) and/or V B ( 2 )) and repeating the process until a 50:50 detector count distribution is obtained. The calibration method can be carried out periodically during QKD system operation to ensure optimum or near-optimum operation of the modulators.

Description:
CLAIM OF PRIORITY 
     This patent application claims priority from U.S. Provisional Patent Application No. 60/549,357, filed on Mar. 2, 2004. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to and has industrial utility in the field of quantum cryptography, and in particular relates to methods for automatically calibrating modulators in quantum key exchange (QKD) systems. 
     BACKGROUND ART 
     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 thus reveal her presence. 
     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,” J. Cryptology 5: 3-28 (1992), and by C. H. Bennett, entitled “Quantum Cryptography Using Any Two Non-Orthogonal States,” Phys. Rev. Lett. 68 2121 (1992). 
     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. 
     The above mentioned publications by Bennett each describe a so-called “one-way” 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 one-way system described in the Bennett 1992 paper is based on two optical fiber Mach-Zehnder interferometers. Respective parts of the interferometric system are accessible by Alice and Bob so that each can control the phase of the interferometer. The interferometers need to be actively stabilized to within a portion of quantum signal wavelength during transmission to compensate for thermal drifts. 
     U.S. Pat. No. 6,438,234 to Gisin (the &#39;234 patent) discloses a so-called “two-way” QKD system that is autocompensated for polarization and thermal variations. Thus, the two-way QKD system of the &#39;234 patent is less susceptible to environmental effects than a one-way system. 
     However, in autocompensated and actively stabilized QKD systems, it is the optics layer that is stabilized or compensated. As it turns out, drifts can and do occur in the electronics necessary to stably operate the QKD system. For example, in a phase-encoding QKD system, if the voltage used to set the phase modulators drifts over time, then the phase imparted to the optical pulses will drift over time. The same is true for polarization modulators in polarization-encoding systems. This drift results in the pulses not having precise phase or polarization modulation, which reduces the ability to detect the encoded pulses. If this drift goes uncompensated, the operation of the QKD system continually diminishes, and can even reach the point where the QKD system can no longer operate. 
     Also, when performing the analysis of the basis measurements under particular QKD protocol (e.g., the BB84 protocol), there needs to be a 50:50 chance of Bob&#39;s detectors detecting signals measured in a basis different from Alice&#39;s basis. To the extent this probability differs from 50:50, an eavesdropper has a potential advantage because the uncertainty associated with a “wrong” basis measurement is reduced. This variation from a 50:50 probability distribution can occur because the modulator basis voltages are not “orthogonal,” i.e., a change in basis voltage by a discrete amount (e.g., from V[−π/4] to V[π/4]) does not result in the modulator providing the corresponding phase difference of π/2. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a two-way QKD system as arranged to provide for calibration of the modulators in Bob and Alice; 
         FIG. 2  is a flow diagram of an example embodiment of the method of performing modulator autocalibration as described in connection with the two-way QKD system of  FIG. 1 ; 
         FIG. 3  is a graph that illustrates the variation in photon count in detectors  32   a  and  32   b  as a function of Alice&#39;s varying modulator voltage V A  for the case where V A =−π/4 corresponds to constructive interference in the detected interfered pulse as indicated by a maximum photon count in detector  32   a  and a minimum photon count in detector  32   b ; and 
         FIG. 4  is a graph that illustrates the variation in photon count in detectors  32   a  and  32   b  as a function of Alice&#39;s varying modulator voltage V A  for the case where V A =3π/4 corresponds to destructive interference in the detected interfered pulse as indicated by a minimum photon count in detector  32   a  and a maximum photon count in detector  32   b.    
     
    
    
     SUMMARY OF THE INVENTION 
     The present invention relates to and has industrial utility in the field of quantum cryptography, and in particular to quantum key distribution (QKD). The invention provides methods for performing phase or polarization modulation calibration of a QKD system. The invention is described in connection with the operation of a two-way QKD system, though the methods are not so limited. 
     As described in detail below, an example embodiment of the invention as applied to a two-way QKD system includes setting Bob&#39;s (timed) modulator voltage V B  to a first positive value (say, V B ( 1 )=V B [π/4]) and then adjusting Alice&#39;s modulator voltage V A  in both the positive and negative directions while exchanging pulses. Thus, the only difference between normal operation of the QKD system and the calibration operation is that the modulators are not randomly modulated. 
     The variation in Alice&#39;s modulator voltage is carried out to find respective overall basis voltages V A ( 1 ) and V A ( 2 ) that in one case correspond to a maximum number of counts in one detector due to constructive interference and in the other case as a maximum number of counts in the other detector due to destructive interference. In the example where V B ( 1 )=V B [π/4], the corresponding basis voltages for Alice are set at V A ( 1 )=V A [−π/4] and V A ( 2 )=V A [3π/4]. 
     Bob&#39;s modulator voltage V B  is then set to a negative value (e.g., V B ( 2 )=V B (−π/4)) and the process repeated to obtain two more nominal basis voltages arid for Alice, namely V A ( 3 )=V A (π/4) and V A ( 4 )=V A [−3π/4]. When all of the basis voltages are set (calibrated), the QKD system is operated to verify orthogonality between the basis voltages. This is accomplished by purposely selecting “incorrect” basis voltage values at Bob and Alice and measuring the probability distribution of detecting a photon at each of two detectors. If the probability distribution is not 50:50, one or more of Bob&#39;s modulator basis voltage values V B ( 1 ) and V B ( 2 ) is/are adjusted and the above-described process repeated until a detector count probability distribution of 50:50 is obtained for the “incorrect” measurement bases. This establishes orthogonality between the established basis voltages and provides calibrated basis voltage values V B ( 1 ) and V B ( 2 ) for Bob and V A ( 1 ), V A ( 2 ), V A ( 3 ) and V A ( 4 ) for Alice. 
     The QKD system is then operated at the calibrated basis voltages, which correspond directly to the proper modulations for Alice&#39;s and Bob&#39;s modulators. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Two-Way QKD System 
       FIG. 1  is a schematic diagram of a two-way QKD system  100 . Bob includes a laser  12  that emits light pulses P 0 . Laser  12  is coupled to a time-multiplexing/demultiplexing (M/D) optical system  104 . M/D optical system  104  receives input pulses P 0  from laser  12  and splits each pulse into two time-multiplexed pulses P 1  and P 2  having orthogonal polarizations. Likewise, later on in the key exchange process (discussed below), optical system  104  receives from Alice the returned pairs of time-multiplexed pulses and combines (interferes) them into a single pulse. 
     Bob also includes a phase modulator MB in M/D optical system  104 . An optical fiber link FL is coupled to M/D optical system  104  and connects Bob to Alice. Bob also includes a voltage controller  44  coupled to modulator MB, and a random number generator (RNG) unit  46  coupled to the voltage controller. 
     Bob also includes two detectors  32   a  and  32   b  coupled to M/D optical system  104 . Bob further includes a controller  50  operatively (e.g., electrically) coupled to laser  12 , detectors  32   a  and  32   b , voltage controller  44  and RNG unit  46 . 
     With continuing reference to  FIG. 1 , Alice includes a phase modulator MA coupled at one end to optical fiber link FL and at the opposite end to a Faraday mirror FM. Alice also includes voltage controller  14  coupled to modulator MA, and random number generator (RNG) unit  6  coupled to the voltage controller. Alice further includes a controller  20  coupled to RNG unit  16  and to voltage controller  14 . 
     Bob&#39;s controller  50  is coupled (optically or electronically) to Alice&#39;s controller  20  via a synchronization link (channel) SL to synchronize the operation of Alice and Bob. In particular, the operation of the phase modulators MA and MB is coordinated by synchronization signals SS that pass from controller  50  to controller  20  (or vice versa, or both ways) over synchronization link SL. In an example embodiment, the operation of QKD system  100 , including the calibration procedure described below, is controlled from either controller  20  or controller  50 . 
     Method of Operation 
     With continuing reference to  FIG. 1 , in the operation of QKD system  100 , Bob&#39;s controller  20  sends a signal S 0  to laser  12 , which in response thereto initiates a relatively strong, short laser pulse P 0 . Laser pulse P 0  is then attenuated by an optional variable optical attenuator VOA  13 B, which is operably coupled to and controlled by controller  50 . The (attenuated) pulse P 0  arrives at M/D optical system  104 , which splits the pulse into two orthogonally polarized pulses, P 1  and P 2 . Pulse P 1  goes directly to optical fiber link FL, while pulse P 2  is delayed and goes through modulator MB, which is not activated at this point. Pulses P 1  and P 2  pass from M/D optical system  104  to optical fiber link FL and travel over to Alice, with pulse P 2  following pulse P 1 . 
     Note also that in another embodiment of system  100 , pulses P 0  and P 1  can be relatively strong pulses that are attenuated by Alice using a VOA  13 A located at Alice, wherein the pulses are attenuated to make them weak (quantum) pulses prior to them returning to Bob. 
     The pulses P 1  and P 2  pass through Alice&#39;s modulator MA and reflect off of Faraday mirror FM, which changes the polarization of the pulses by 90°. As the pulses travel back through modulator MA, Alice lets the first pulse P 1  pass therethrough unmodulated, but modulates the phase (i.e., imparts a phase shift φ A  to) second pulse P 2 . It should be noted here that Alice could also choose to modulate pulse P 1 . Since pulses P 1  and P 2  are later interfered, it is not the phase imparted to each pulse that matters, but rather the relative phase between the two pulses. 
     The timing of the activation of modulator MA to coincide with the arrival of pulse P 2  is provided by the synchronization signal SS shared between controllers  20  and  50 , as described in greater detail below. In an example embodiment illustrated schematically in  FIG. 1 , the modulation is carried at Alice out by controller  20  providing a well-timed signal S 1  to RNG unit  16 , which provides a signal S 2  representative of a random number to voltage controller  14 . Voltage controller  14  then sends a timed voltage signal V A  randomly selected from a set of basis voltages (e.g., V[+3π/4], [V−3π/4], V[+π/4], and V[−π/4]) to modulator MA to randomly set the phase modulation to a corresponding basis phase, e.g., +3π/4, −3π/4, π/4 or −π/4. The selected voltage value V A  (or the corresponding random number) is reported to controller  20  and the (corresponding) voltage information (or the corresponding phase information) stored therein. For the sake of illustration, the timing of the voltage signal V A  can be considered as being based on signal S 2 . In practice, a separate timing signal (not shown) from controller  20  may be used. 
     The two pulses P 1  and P 2  then travel back to Bob and to M/D optical system  104 . Pulse P 2  passes unaltered through the optical system but pulse P 1  passes through modulator MB and receives a phase shift φ B . The timing of the modulation of pulse P 1  by phase modulator MB is provided by the synchronization signal SS shared between controllers  20  and  50 . The modulation of pulse P 1  by modulator MB is carried out by controller  50  providing a well-timed signal S 3  to RNG unit  46 , which provides a signal S 4  representative of a random number to voltage controller  44 . Voltage controller  44  then sends a timed voltage signal V B  randomly selected from a set of voltages (e.g., V[+π/4] or V[−π/4]) to modulator MB to randomly set the phase modulation to a corresponding basis phase, e.g., +π/4 or −π/4. The selected voltage value V B  (or the corresponding random number) is reported to controller  50  and the voltage information (or corresponding phase information) stored therein. Again, for the sake of illustration, the timing of voltage signal V B  may be considered as being based on signal S 3 . In practice, a separate timing signal (not shown) from controller  50  may be used. 
     Further, when pulses P 1  and P 2  enter M/D optical system  104 , pulse P 2  passes through without a delay, but pulse P 1  is delayed by an amount equal to that originally imparted to pulse P 2 . M/D optical system then interferes the two pulses P 1  and P 2 . 
     The single-photon detectors  32   a  and  32   b  are arranged so that constructive interference (φ A −φ B =0) between pulses P 1  and P 2  is detected by detector  32   a , while destructive interference (φ A −φ B =π) is detected by detector  32   b . When Bob imparts the same basis phase as Alice, a count in detector  32   a  indicates binary 0 and a count in detector  32   b  indicates binary 1. However, when Bob&#39;s basis phase is different from Alice&#39;s, there is no correlation in the detection of interfered pulses P 1  and P 2 , and the interfered signal is detected in either detector  32   a  or  32   b  with equal probability (i.e., interfered the pulse has a 50:50 chance of being detected in either detector). 
     The process of exchanging pairs of pulses is repeated many times so that a large number of photons are detected in detectors  32   a  and  32   b . Alice and Bob then publicly exchange information about their choice of basis modulations, and perform other processing of exchanged basis information (e.g., key sifting, error correction and privacy amplification) to establish a key that can be used to securely encode information. 
     Modulator Timing Set-Up 
     The description above is based on the idealized operation of a two-way QKD system. However, in practice, such systems do not automatically operate in an ideal state. Further, a commercially realizable system must first be set up to operate at or close to an ideal state, and then must be able to compensate for changes in its operating state to ensure ongoing operation in or close to the ideal operating state. The autocalibration methods set forth below presume that the modulator timing in QKD system  100  has been established via synchronization channel SL via synchronization signals SS. 
     Modulator Autocalibration 
     As mentioned above, drifts can and do occur in the electronic layers of QKD systems during system operation. In a commercially viable QKD system, the drifts need to be compensated so that the system can operate continuously. Accordingly, a method of performing modulator autocompensation is now described in connection with two-way QKD system  100 . Note that the voltages used to set the modulators to a select phase are referred to herein as a “basis voltages.” 
     With continuing reference to  FIG. 1  and also to flow diagram  400  of  FIG. 2 , in  402  controller  50  instructs voltage driver  44  to provide a first select basis voltage—say V B ( 1 )=V B [π/4]—to phase modulator MB. This process is carried out (schematically) by sending a control signal SC 1  from controller  50  to voltage driver  44 . Control signal SC 1  is timed to modulate pulse P 1  when it returns from Alice. This voltage depends on the type of modulator, but may be, for example, 1 volt. Voltage V B ( 1 )=V B [π/4] sets modulator MB to a nominal phase setting of π/4. 
     In  404 , Bob generates and sends pulses P 1  and P 2  through optical fiber link FL over to Alice. While pairs of pulses P 1  and P 2  are being sent back and forth between Bob and Alice, Alice activates her modulator with voltage signal V A . This process is illustrated schematically by sending a control signal SC 2  to voltage driver  14  from controller  20 . The voltage signal V A  is timed to modulate pulse P 2 . Thus, the calibration operation of QKD system  100  is similar to the normal key-exchange operation, except that the modulations are not randomly selected but are instead set directly by the respective controllers. 
     Alice&#39;s voltage V A  is varied in the negative direction during the exchange of pulses. For each voltage value V A , a number of pulse pairs P 1  and P 2  (e.g., 10 6 ) are exchanged and the number of interfered signals detected in detectors  32   a  and  32   b  is recorded in controller  50 . 
     Voltage V A  is so varied until the total (relative) phase shift φ T =φ A +φ B  imparted to the pulses is 0 (constructive interference) is observed as a maximum photon count for the returned interfered pulses being detected in detector  32   a , and a minimum photon count in detector  32   b . This voltage is assigned a basis value, which in the present example is V A ( 1 )=V A [−π/4]. 
       FIG. 3  is a graph that illustrates the variation in photon count N in detectors  32   a  and  32   b  as a function of voltage V A . The lack of an absolute maximum and minimum in the photon count results from detector dark count. In practice, because of the detector dark count, it is easier to measure the minimum photon count in detector  32   b  rather than the maximum photon count in detector  32   a  to establish the basis voltage V A ( 1 )=V A (−π/4) 
     This basis voltage is then set to be V A ( 1 )=V A [−π/4] in voltage driver  14 , and this value is stored in the controller. 
     It is worth noting that in  404 , the pulses P 1  and P 2  returning to Bob from Alice are preferably weak (quantum pulses). However, these pulses could be strong pulses if used in combination with photodiode detectors arranged at Bob suitable for detecting strong pulses. For the sake of simplicity, however, quantum pulses are preferred, since the detectors  32   a  and  32   b  are single-photon detectors. 
     In  406 , the voltage V A  provided to Alice&#39;s modulator MA is again varied as described above, but in the positive voltage range, until the total relative phase shift imparted to the pulses is π (destructive interference) as indicated by a maximum photon count in detector  32   b  and a minimum photon count in detector  32   a . Again, in practice it is easier to measure the minimum photon count in detector  32   a  to establish the corresponding basis voltage V A ( 2 )=VA[3π/4]. This voltage is then set to V A ( 2 )=VA[3π/4] in voltage driver  14  and the result stored in controller  20  as described above. 
     At this point, Bob&#39;s voltage has been set initially at V B ( 1 )=V B [π/4] and Alice&#39;s corresponding basis voltages V B ( 1 )=V A [−π/4] and V A ( 2 )=V A [3π/4] have been established. 
     In  408 , Bob&#39;s modulator voltage V B  is changed via control signal SC 1  to the remaining basis voltage, which in this example case is V B ( 2 )=V B [−π/4]. Acts  404  and  406  are then repeated to establish V A ( 3 )=V A [π/4] by varying V A  in the positive voltage range, and to establish V A ( 4 )=V A [−3π/4] by varying the voltage in the negative voltage range. Once this is accomplished, all of the (initial) basis voltages needed for modulating Bob&#39;s modulator MB and Alice&#39;s modulator MA are established, and the information stored in the respective controllers. 
     Once the basis voltages for the modulators are established per above, the orthogonality of the voltages needs to be checked. Thus, in  410 , QKD system is operated with the modulators MA and MB intentionally set at fixed basis voltages that correspond to Bob making an “incorrect” basis measurement, i.e., the total phase φ T  imparted to the pulses is not a multiple of π. This is accomplished via respective control signals SC 1  and SC 2  sent from respective controllers  50  and  20  to respective voltage drivers  44  and  14 . For example, Bob&#39;s basis voltage is set to V B [π/4] and Alice&#39;s basis voltage is set at V A [π/4], so that Bob&#39;s modulator MB is set to impart a phase φ B =+π/4 and Alice&#39;s modulator is set to impart a phase φ A =π/4. This set-up yields a total imparted (nominal) relative phase of φ T =π/2 between the pulses. 
     The distribution of counts in detectors  32   a  and  32   b  is then measured and assessed. Ideally, the count distribution should be equal since the probability of a count occurring in each detector should be 50:50 when Bob selects the “incorrect” phase basis. If in  410  the count probability is found to be equal (i.e., 50:50), then the basis voltages are orthogonal and represent calibrated basis voltages for modulators MB and MA. 
     On the other hand, the initially established basis voltages may be found not to be orthogonal. Thus, if in  410  the number of counts in detector  32   a  is greater than that recorded by detector  32   b , then in  412  Bob&#39;s modulator voltage V B [π/4] is increased, and if it is less than that recorded by detector  32   b , then in  412  Bob&#39;s modulator voltage V B [π/4] is decreased. In  414 , acts  406  through  410  are repeated until the ideal 50:50 detector count probability distribution is achieved. This confirms orthogonality in the basis voltages. 
     Performing the above acts yields calibrated basis voltages V B ( 1 ) and V B ( 2 ) for Bob&#39;s modulator MB and calibrated voltages V A ( 1 ), V A ( 2 ), V A ( 3 ) and V A ( 4 ) for Alice&#39;s modulator MA. The calibrated basis voltage values are stored in their respective voltage drivers  44  and  14  (or in their respective controllers  50  and  20 ) so that control signals S 3  and S 2  sent from respective RNG units  46  and  16  to the voltage drivers (or alternatively, control signals sent from the controllers to the voltage drivers) trigger the proper basis voltage value and thus the proper phase modulation. 
     The QKD system is now ready for ideal operation. For security reasons, the above-described procedures are preferably performed when Alice and Bob and optical fiber link FL are all in a secure location so there is no eavesdropper to alter the calibration. However, for the sake of necessity, the above-described procedures may need to be performed in the field even though this presents a security risk. 
     On-Going Modulator Autocalibration 
     An example embodiment of the modulator autocalibration method of the present invention includes monitoring the counts in each detector that result from an incorrect basis measurement during the normal operation of the QKD system. As mentioned above, this count distribution should be 50:50 during system operation. After performing the QKD protocol, deviations from this count distribution can be used as a diagnostic tool. When other sources of error are eliminated, this parameter can be used as a trigger to initiate the above-described autocalibration process. This allows the modulators of the QKD system to be calibrated on an on-going basis or periodically as needed. 
     In an example embodiment, the modulator calibration methods are accomplished by including in controllers  20  and  50  software embodied in a tangible medium (e.g., a hard drive, not shown) that has instructions for carrying out the method discussed above. 
     In the foregoing Detailed Description, various features are grouped together in various example embodiments for ease of understanding. 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. 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. Accordingly, other embodiments are within the scope of the appended claims.