Abstract:
Systems and methods for performing quantum key distribution (QKD) that allow for an improved signal-to-noise ratio (SNR) when providing active compensation for differences that arise in the system&#39;s relative optical paths. The method includes generating at one QKD station (Alice) a train of quantum signals having a first wavelength and interspersing one or more strong control signals having a second wavelength in between the quantum signals. Only the quantum signals are modulated when the quantum and control signals travel over the first optical path at Alice. The quantum and control signals are sent to Bob, where only the quantum signals are modulated as both signal types travel over a second optical path at Bob. The control signals are directed to two different photodetectors by an optical splitter. The proportion of optical power detected by each photodetector represents the optical path difference between the first and second optical paths. This difference is then compensated for via a control signal sent to a path-length-adjusting element in one of the optical paths. The control signals provides a high SNR that allows for commercially viable QKD system that can operate with a high qubit rate and a small qubit error rate (QBER) in the face of real-world sources of noise.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates generally to quantum cryptography, and in particular to actively stabilized quantum key distribution (QKD) systems. 
       BACKGROUND ART 
       [0002]    QKD involves establishing a key between a sender (“Alice”) and a receiver (“Bob”) by using either single-photons or weak (e.g., 0.1 photon on average) optical signals (pulses) called “qubits” or “quantum signals” transmitted over a “quantum channel.” Unlike classical cryptography whose security depends on computational impracticality, the security of quantum cryptography is based on the quantum mechanical principle that any measurement of a quantum system in an unknown state will modify its state. As a consequence, an eavesdropper (“Eve”) that attempts to intercept or otherwise measure the exchanged qubits will introduce errors that reveal 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 (“the &#39;410 patent”) and in the article by C. H. Bennett entitled “Quantum Cryptography Using Any Two Non-Orthogonal States”, Phys. Rev. Lett. 68 3121 (1992), both of which are incorporated by reference herein. 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 (“Bouwmeester”), which is incorporated by reference herein by way of background information. 
         [0004]    The typical so-called “one way” QKD system, such as disclosed in the &#39;410 patent, uses a “shared interferometer” consisting of a pair of unbalanced interferometers with precisely matched differential optical path lengths. The first unbalanced interferometer, located with Alice, splits a single photon into two spatially separated wave packets and the second unbalanced interferometer, located in Bob, brings the two wave packets together and interferes them. Because the two unbalanced interferometers are located remotely from each other, slight mismatches in the differential optical path lengths can arise from local environmental effects, including thermal fluctuations, acoustic noise, and vibrations. A mismatch in the differential optical path lengths result in a phase error that reduces the degree of interference of the single-photon-level optical pulses (“quantum pulses”). This in turn increases the quantum bit-error rate (QBER), which reduces the efficiency of the QKD process. 
         [0005]    A one-way QKD systems needs to be stabilized to maintain the optical path-length balance of Alice and Bob&#39;s shared interferometer to within a fraction of the wavelength (e.g., ˜30 nm for 1.5 um light). Generally, this can be accomplished by passing “control” pulses (i.e., multi-photon “classical” optical pulses) through the shared interferometer at one QKD station (e.g., Alice) and detecting it at the output of the other QKD station (e.g., Bob). The QKD system is configured so that the classical optical pulses follow the same optical path traversed by the quantum pulses. Consequently, it is possible to monitor the phase error superimposed upon the qubits by observing the interference of the classical signals at the output of the interferometer. Using error signals generated by these interference patterns, it is possible to produce negative feedback for an actuator adapted to counteract this phase error. In response to the feedback signal, the actuator creates a compensating phase change at a single location (e.g., at Bob) to restore the optical path length balance. An example of an actively stabilized one-way QKD system is described in WIPO PCT Patent Application Publication No. WO2005067189 A1, entitled “Active stabilization of a one-way QKD system,” published on Jul. 21, 2005, which patent application is incorporated by reference herein. 
         [0006]    One prior art approach to actively stabilizing a QKD system uses relatively weak (i.e., on the order of 25 photons) synchronous control signals of the same wavelength as the quantum signal. Since these classical control signals are at the same wavelength as the quantum signals, only time multiplexing can be used to separate them. The control signal intensity must be kept close to the single photon level when using gated-Geiger-mode avalanche photodiodes (APDs) as single photon detectors (SPDs). Since SPDs are still sensitive photo-detectors during the time intervals between gating pulses, any classical signals reaching them generate an enormous number of electrons, some of which become trapped in the APD junction and cause spontaneous avalanches as soon as gating pulses are applied. This causes a very high effective dark count rate. Because of its low intensity, the control signal must also be detected by its own, separate single photon detector(s). The control and quantum signal SPDs both share the same limitations so they are operated at the same repetition rate, namely, one stabilization pulse per quantum bit period. 
         [0007]    Due to the binary output nature of single photon detectors, a meaningful feedback signal useful for compensating for interferometer phase drift can only be made by integrating over a relatively large number of samples (e.g., 100 samples). This increases the signal-to-noise ratio (SNR) at the expense of tracking bandwidth. For a qubit rate of 100 KHz and a 100-sample integration time, the system can be compensated only to 1 ms, which corresponds to rather weak 1 KHz vibrations. If the vibration amplitude is stronger, the system may not be able to track it, which leads to an increase in the QBER. 
         [0008]    Another prior art approach uses a separate wavelength for the control signal. This allows the use of higher power control pulses because wavelength filtering prevents these signals from arriving at the SPDs. Higher power control signals allow the use of linear detection of the control signal, relieving the need to integrate over many periods. However, this approach uses a control signal pulse rate significantly lower than the quantum signal pulse rate (by a factor of 1/10). While this may provide satisfactory operation for laboratory and experimental conditions, it does not provide sufficient bandwidth for a commercially viable QKD system that requires tracking high-frequency, high-amplitude vibrations, such as for example, those coupled into the interferometers by system fan noise. 
         [0009]    Another prior art approach is to use a planar lightwave circuit (PLC) based unbalanced Mach-Zehnder interferometers for Alice and Bob&#39;s interferometers. Each interferometer is integrated onto a silica chip that is temperature stabilized to 0.01° C., which provides sufficient stability for low QBER. The main disadvantages of this approach, however, are the higher excess loss of these interferometers compared to fiber based interferometers and the fact these components are not readily available and are difficult to manufacture. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention is directed to systems and methods for performing quantum key distribution (QKD) that allow for an improved signal-to-noise ratio (SNR) when providing active compensation of the system&#39;s relative optical paths. The method includes generating a train of quantum signals having a first wavelength and interspersing at least one and preferably a relatively large number of strong control signals having a second wavelength in between the quantum signals. Only the quantum signals are modulated when the quantum and control signals travel over the first optical path at Alice. The quantum and control signals are sent to Bob, where only the quantum signals are modulated as both signal types travel over a second optical path at Bob. The control signals are directed to two different photodetectors by an optical splitter. The proportion of optical power detected by each photodetector represents the optical path difference (i.e., phase error) between the first and second optical paths. This difference is then compensated via a control signal sent to a path-length-adjusting (PLA) element in one of the optical paths. The strong control signals provides a high SNR that allows for commercially viable QKD system that can operate with a high qubit rate and a small qubit error rate (QBER) in the face of real-world sources of noise. Example embodiments using a fiber-based, phase-modulated QKD system and a PLA element in the form of an actuator residing in a section of optical fiber and that can change the phase of light passing therethrough, are discussed in detail below. 
         [0011]    Additional features and advantages of the invention will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the invention as described herein, including the detailed description which follows, the claims, as well as the appended drawings. 
         [0012]    It is to be understood that both the foregoing general description and the following detailed description present embodiments of the invention, and are intended to provide an overview or framework for understanding the nature and character of the invention as it is claimed. The accompanying drawings are included to provide a further understanding of the invention, and are incorporated into and constitute a part of this specification. The drawings illustrate various embodiments of the invention, and together with the description serve to explain the principles and operations of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  is a generalized schematic diagram of an actively compensated QKD system according to the present invention; 
           [0014]      FIG. 2  is a schematic diagram of an example embodiment of Alice of the QKD system of  FIG. 1  for carrying out the active-stabilization method of the present invention; 
           [0015]      FIG. 3  is a schematic diagram of an example embodiment of Bob of the QKD system of  FIG. 1  for carrying out the active-stabilization method of the present invention; and 
           [0016]      FIG. 4  is a schematic timing diagram of the optical signals as present on the input optical fiber section at Alice&#39;s interferometer, illustrating the relatively large number of optically strong control signals for each quantum signal so as to provide a large signal-to-noise ratio (SNR) when measuring the phase error and generating the feedback control signal to correct the measured phase error based on the optical power detected from the classical signals rather than via SPD “clicks.” 
       
    
    
       [0017]    The various elements depicted in the drawing are merely representational and are not necessarily drawn to scale. Certain sections thereof may be exaggerated, while others may be minimized. The drawing is intended to illustrate an example embodiment of the invention that can be understood and appropriately carried out by those of ordinary skill in the art. Where convenient, the same or like elements are given the same or like reference numbers. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0018]      FIG. 1  is a schematic diagram of an actively stabilized QKD system  10  according to the present invention. QKD system  10  includes a QKD station Alice and a QKD station Bob that are optically coupled. In the example embodiment of  FIG. 1 , Alice and Bob are optically coupled by an optical fiber link FL. Alice and Bob communicate by encoded single-photon-level quantum signals QS having a wavelength λ Q . The encoding may be any type of encoding that changes the state of the photon. Usually, polarization encoding or phase encoding is used, as described in Bouwmeester. The present invention applies to any type of encoding scheme and QKD system that requires active stabilization in order to maintain the qubit error rate (QBER) at an acceptable level. For example, in a polarization-based QKD system, a polarized control signal is sent over the optical fiber link FL and is used to determine changes in the polarization state over the QKD system optical path. 
         [0019]    In the present invention, the active stabilization utilizes classical optical signals as control signals CS that have wavelength λ C ≠λ Q  so that strong control signals can be used, as described below. 
       Phase-Encoding QKD System 
       [0020]    An example embodiment of the active-stabilization method of the present invention is now described in connection with a phase-based QKD system  10  as illustrated in  FIGS. 2 and 3 . As mentioned above and as will be apparent to one skilled in the art, the present invention applies to any actively compensated QKD system that employs optical signals separate from the quantum signals to measure system drift and to correct the drift. 
       Alice 
       [0021]    With reference to  FIG. 2 , Alice includes a “quantum light source”  20  adapted to generate quantum signals QS of wavelength λ Q . Alice also includes a classical (i.e., multi-photon) light source  22  adapted to generate control signals CS of wavelength λ C  that are used for compensating the shared interferometer, as discussed below. 
         [0022]    In one example embodiment, quantum light source  20  is in the form of a pulsed laser that is optically coupled to an attenuator  24  that attenuates output laser pulses P 0  to create quantum signals QS in the form of weak pulses (i.e., one photon or less, according to Poissonian statistics). In another example embodiment, quantum light source  20  is a single-photon light source that generates true single-photon quantum signals QS (which in this case are the same as output laser pulses P 0 ). For the case where the output of quantum light source  20  is already at the single photon level, attenuator  24  is not needed. 
         [0023]    Alice further includes a wavelength division multiplexer (WDM)  40 A optically coupled to quantum light source  20  and to control signal light source  22 . WDM  40 A is also optically coupled to Alice&#39;s unbalanced interferometer  50 A via an input optical fiber section FA IN . Interferometer  50 A further includes an optical splitter  56 A to which optical fiber section FA IN  is coupled and that forms two interferometer arms  62 A and  64 A that each includes a faraday mirror FM. A phase modulator MA is arranged in arm  64 A and an optical delay loop ODL A  is arranged in arm  62 A forming an associated first differential optical path length ΔL A  that can change due to environmental effects at Alice. The splitter  56 A splits each input pulse and upon exiting the interferometer one of the pulses is time delayed by ΔT=2·n·ΔL A /c where n is the index of refraction of the fiber, c is the speed of light in vacuum, and the factor of “2” is the result of the double pass through the delay loop. Modulator MA is adapted to impart a randomly selected phase to the quantum signal QS as part of the QKD process. Interferometer  60 A is optically coupled at optical splitter  56 A to optical fiber link FL via an output optical fiber section FA OUT  and a second WDM  70 A. A synchronization light source  80  is also optically coupled to optical fiber link FL via WDM  70 A and generates synchronization signals SS that serve to synchronize the operation of Alice and Bob. 
         [0024]    Alice also includes a controller CA that is electrically coupled to modulator MA, quantum light source  20 , control light source  22 , synchronization light source  80  and optical attenuator  24 , if such is present. An optical isolator  82  is arranged between optical splitter  56 A and WDM  70 A to ensure that light travels only one way from optical splitter to WDM  70 A. 
       Bob 
       [0025]    Bob includes a WDM  70 B optically coupled at its input end to optical fiber link FL and at its output end to a synchronization detector  100  and to Bob&#39;s interferometer  50 B. Detector  100  is used to detect synchronization signals SS. 
         [0026]    Bob&#39;s interferometer  50 B includes an optical splitter  56 B that, like Alice, has associated therewith input and output optical fiber sections FB IN  and FB OUT . Optical splitter  56 B forms two interferometer arms  62 B and  64 B that each includes a Faraday mirror FM. Interferometer  60 B has associated therewith a second differential optical path length ΔL B  formed by the presence of ODL B  arranged together with an electronically controlled path-length-adjusting (PLA) member  110  in arm  62 B, such as an actuator. PLA member  110  is used to adjust the differential optical path length ΔL B  in response to a feedback control signal S C . A phase modulator MB is arranged in arm  64 B and is used to impart a randomly selected phase to the quantum signal QS as part of the QKD process. Optical splitter  56 B has two outputs, with one output going to a first SPD SPD 1  and a first photodetector PD 1  via fiber section FB IN , a circulator  120  and a multiplexer  130 . The other output goes to a second SPD SPD 2  and a second photodetector PD 2  via FB OUT  and multiplexer  132 . 
         [0027]    The differential optical path length ΔL B  of interferometer  50 B is required to exactly match ΔL A  of interferometer  50 A to ensure ideal interference of the quantum signals. The actual values of ΔL A  and ΔL B  can vary as a function of the different environmental effects at Alice and Bob. However, at least one of the optical paths (here, the optical path at Bob) must be actively adjusted so that ΔL A =ΔL B . 
         [0028]    Bob also has a controller CB, which in an example embodiment includes a processing unit  140 , a computer readable medium  141 , and other processing electronics (not shown) such as, for example, a field-programmable gate array (FPGA), adapted to control the operation of Bob (e.g., gating SPD 1  and SPD 2 ) in a manner that is synchronized with the operation of Alice. Controller CB is operably coupled to SPD 1 , SPD 2 , PD 1 , PD 2 , synchronization detector  100 , modulator MB, and PLA member  110 . The instructions for controlling the operation of Bob can be stored, for example, on computer-readable medium  141 , which in an example embodiment constitutes part of an FPGA. 
       Method of Operation 
       [0029]    With reference to  FIG. 2  and  FIG. 3 , system  10  operates as follows. Controller CA sends a control signal S 80  to synchronization light source  80 , which in response thereto emits synchronization signals SS. Synchronization signals SS are multiplexed onto optical fiber link FL via WDM  70 A and travel over to Bob, where they are demultiplexed by WDM  70 B and detected by sync detector  100 . Sync detector  100  generates an electrical synchronization signal S 100  that is received by Bob&#39;s controller CB and is processed by processing unit  140  to establish the system timing and synchronization. 
         [0030]    Alice sends control signals S 20  and S 22  to quantum light source  20  and control light source  22 , respectively, to cause these light sources to generate respective quantum signals QS and control signals CS. Here, control signals CS are not relatively weak (e.g., tens of photons) but rather are relatively strong (e.g., a thousand, many thousands, tens of thousands or millions of photons per signal). The allowable intensity of these pulses is dependent on the isolation provided by multiplexers  130  and  132  (which serve as filters), as well as the responses of the two SPDs. 
         [0031]    Quantum and control signals QS and CS enter WDM  40 A and are multiplexed thereby and enter Alice&#39;s interferometer  50 A. Interferometer  50 A serves to split each optical pulse that enters it into two pulses separated by time delay ΔT=2·n·ΔL A /c where n is the index of refraction of the fiber, c is the speed of light in vacuum, and the factor of “2” is the result of the double pass in the delay loop. The quantum and control pulses then exit interferometer  50 A via output fiber FA OUT . 
         [0032]      FIG. 4  is a schematic diagram illustrating the quantum and control signals QS and CS as multiplexed onto the input optical fiber section FA IN  of interferometer  50 A. The quantum signals QS, with period T Q , have a low duty cycle which allows one or more control signals CS to fit between each quantum signal QS and be synchronous therewith. In an example embodiment, a relatively large number of control signals CS (e.g., greater than about 50, and preferably between from 50 to 100) are used when the time interval between the quantum signals permits. The selection of the control signal pulse period T CS  is dependent on the time delay ΔT induced by interferometer  50 A and in the cleanest implementation is set so that T CS &gt;2·ΔT. This condition prevents one pulse from overlapping the previous delayed pulse upon exiting Alice&#39;s or Bob&#39;s interferometer. 
         [0033]    Interferometer  50 A also contains a phase modulator MA which is able to modulate the relative phase between any of the two time delayed pulses. For the security of the quantum key exchange it is vital that the phase modulation is applied only to the quantum signals. If the same phase encoding information were also imparted upon the control signals, then an eavesdropper could easily gain knowledge of the quantum key by measuring these classical signals while producing no indication of eavesdropping. 
         [0034]    To prevent this, controller CA controls the output timing of the quantum and control signals QS and CS so that they do not overlap. Furthermore, the control signal transmission is interrupted for a brief period of time associated with the modulator activation at Alice and Bob called the modulator timing window TW (i.e., this signal lies outside of the timing window provided by modulator activation signal S A ). This is so that control signals CS are not passing through the modulators MA or MB while they are being activated to modulate the quantum signal QS. Quantum signal QS thus becomes a once-modulated quantum signal QS′ having received a phase modulation φ modA . The total phase difference between the two time delayed quantum signal pulses exiting Alice is Δφ Q =4π·n·ΔL A /λ Q −φ modA . The corresponding phase shift seen by the control signals which are not modulated is Δφ C =4π·n·ΔL A /λ C . 
         [0035]    Control signals CS and the associated once-modulated quantum signal QS′ exit interferometer  50 A on output optical fiber section FA OUT  and are optically coupled onto optical fiber link FL via WDM  70 . The quantum signal QS and the associated control signals CS then travel over to Bob via optical fiber link FL. 
         [0036]    The quantum signal QS and the associated control signals CS enter Bob&#39;s interferometer  50 B via input optical fiber section FB IN . The once-modulated quantum signal QS′ is modulated again, receiving phase φ modB  by modulator MB via a corresponding timed modulator activation signal SB provided by controller CB, thereby forming a twice-modulated quantum signal QS″. The total phase difference between the two interfering quantum pulses upon reaching coupler  56 B and interfering is Δφ Q =(4π·n·ΔL A /λ Q −φ modA )−(4π·n·ΔL B /λ Q −φ modB )=4π·n·(ΔL A −ΔL B )/λ Q +φ modB −φ modA . Again, the timing window TW leaves the control signals unmodulated so the phase difference between the interfering control pulses is simply Δφ C =4π·n·(ΔL A −ΔL B )/λ C . The operation of the control signal ensures that ΔL A −ΔL B =0 and remains stable which is accomplished by maintaining Δφ C  at a constant value and checking the condition Δφ C =Δφ C  when φ modB −φ modA =0. 
         [0037]    Twice-modulated quantum signal QS″ and the associated control signals CS exit interferometer  60 B either via FB IN  or FB OUT , depending on the overall phase modulation imparted to quantum signal QS″. For constructive interference, quantum signal QS″ is directed by optical splitter  56 B via fiber section FB IN  to circulator  120 , which directs this signal to WDM  130  and to SPD 1 . Upon detecting a photon, SPD 1  in turn generates a first detection signal (click) SD 1  that is provided to controller CB. Likewise, for destructive interference, quantum signal QS″ is directed by optical splitter  56 B to output optical fiber section FB OUT , which directs this signal to WDM  132  and to SPD 2 . SPD 2  in turn generates a second detection signal (click) SD 2  that is provided to controller CB. 
         [0038]    The many control signals CS associated with the quantum signal QS are directed equally by optical splitter  56 B to FB IN  and FB OUT  and to photodetectors PD 1  and PD 2  associated therewith when the OPL A =OPL B . To the extent OPL A ≠OPL B , then the amount of optical power directed to photodetectors PD 1  and PD 2  depends on the relative phase difference imparted to the control signals CS as they traversed the two interferometers. Corresponding photodetector signals SP 1  and SP 2  are provided to controller CB and are representative of the corresponding amounts of optical power detected at photodetectors PD 1  and PD 2  from the control signals CS. The detected control signals are then used to establish the phase error between interferometers  50 A and  50 B and to generate control (feedback) signal SC that causes PLA member  110  to compensate for the measured phase error. 
         [0039]    The relatively large optical power associated with control signals CS, combined with their relatively large number per quantum signal, provides a very high SNR for the control signals. Since these signals are used to generate control signals SC to PLA member  110  as feedback signals, the high SNR makes the feedback process more robust and thus is able to better maintain a high extinction ratio for the coupled interferometers  50 A and  50 B. It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit and scope of the invention. Thus it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.