Abstract:
Systems and methods for enhanced quantum key distribution (QKD) using an actively compensated QKD system. The method includes exchanging quantum signals between first and second QKD stations and measuring the quantum signal error. An error signal S E  representative of the system visibility error is then generated. An error-signal threshold S TH  that defines a system visibility error limit is then selected. Those qubits measured with the condition S E &gt;S TH  are called “above-threshold” qubits, while those qubits measured with the condition S E ≦S TH  are called “below-threshold” qubits. Only below-threshold qubits are stored and used to form the final quantum key. This is accomplished by sending a blanking signal S B  to the memory unit where the qubits are stored. The blanking signal prevents above-threshold qubits from being stored therein. The raw quantum key so formed has few errors and thus forms a longer final quantum key for a given number of exchanged quantum signals.

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, and systems and methods for forming quantum keys using such 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). 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, use a “shared interferometer” that includes two interferometer halves, with one half at Alice and one half at Bob. Because the two interferometer halves are located remote from each other, differences in the optical path length of the interferometer halves can arise from local environmental effects. A difference in the optical path length, known as “phase error,” reduces the interference visibility (“system visibility”) of the single-photon-level optical pulses (“quantum pulses”), which is detrimental to the efficiency of the QKD process. 
         [0005]    Accordingly, the typical one-way QKD systems need to be actively stabilized in order 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 μm light). This can be done, for example, by passing “classical” pulses (i.e., multi-photon 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 thus 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]    When faced with high-frequency or high-amplitude disturbances, the feedback system&#39;s tracking range and bandwidth limitations may allow the shared interferometer to momentarily (e.g. over multiple qubit intervals) fall out of balance. In some cases these limitations are manifested by operating near the limits of the actuator range. Due to the periodic behavior of optical interference, the actively stabilized interferometer may have several stable modes of operation. Thus, in the case where the operating range of the actuator covers multiple modes, one solution to contending with limited actuator range is to “reset” the actuator to the center of its operating range when it comes too close to one of the range limits. However, depending on the implementation of this process and/or the speed of the actuator, resetting may cause a sudden spike (“glitch”) in phase error as the actuator hops across several modes and re-stabilizes itself at a mode near the midpoint of its operating range. These phase errors in turn are projected onto the quantum signal and thus leads to increased QBER. 
         [0007]    Ideally, the control system used in one-way QKD systems will have sufficient bandwidth and range to eliminate any and all phase perturbations that arise. Realistically, this may not always be possible because there are likely other design tradeoffs that prevent such ideal performance. Among these are the insertion loss of these components, the permissible power level of the classical feedback signal, and cost restrictions. It is also conceivable that the QKD system may be employed in an environment where it is subjected to somewhat frequent high amplitude vibrations, such as a mobile military platform. In all of these cases the feedback system alone may not be capable of continuously eliminating the time-varying phase error. This is significant because each erroneous quantum signal bit leads to the loss of multiple error-free bits that are consumed in the error correction and privacy amplification processes. 
       SUMMARY OF THE INVENTION 
       [0008]    One aspect of the invention is a method of forming a quantum key by exchanging quantum signals between first and second QKD stations of an actively stabilized QKD system. The method includes using classical stabilization pulses to monitor the system visibility while quantum signals are being exchanged. The system visibility is the ability of the system to faithfully discriminate between two orthogonal quantum states. The method also includes generating an error signal S E  proportional to the degree of system visibility reduction. The method further includes setting an error-signal threshold S TH  that defines an upper bound for the allowable system visibility reduction. The method also includes detecting the quantum signals to form qubits based on the quantum signals, and forming a raw quantum key by storing only below-threshold qubits—that is, qubits for which S E ≦S TH . 
         [0009]    Another aspect of the invention is a receiving QKD station of an actively stabilized QKD system adapted to exchange quantum signals over an optical path. The receiving QKD station includes a controller designed to track the system visibility during the exchange of quantum signals and generate therefrom i) an error signal S E  representative of any reduction in the system visibility, and ii) a blocking signal S B  corresponding to quantum signal measurements taken while S E &gt;S TH , wherein S TH  is a decision threshold signal corresponding to the maximum allowable system visibility degradation. The receiving QKD station also includes a memory unit in the controller adapted to store qubits, the memory unit being further adapted to perform “signal blanking,” wherein the memory unit receives the blocking signal S B  and in response thereto blocks the storing of qubits associated with above-threshold qubits so that the memory unit only stores below-threshold qubits for which S E ≦S TH . 
         [0010]    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. 
         [0011]    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 
         [0012]      FIG. 1  is a schematic diagram of a general QKD system; and 
           [0013]      FIG. 2  is a schematic diagram of the QKD system adapted to provide for active compensation and SPD signal blanking. 
       
    
    
       [0014]    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 
       [0015]      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. 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. In an example embodiment, such active stabilization utilizes classical optical signals CS that have the same or similar wavelength as the quantum signal QS. For example, in a polarization-based QKD system, a polarized classical 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. 
         [0016]    In an actively stabilized QKD system  10 , errors are introduced in the state of the quantum signals as the system drifts from its optimum operating state due to, for example, environmental effects such as temperature changes or vibrations. Such drifts occur even in actively stabilized system because the active stabilization scheme cannot be made to respond infinitely fast to system changes. This is particularly true where the error-adjusting elements have a relatively slow response time when compared to the qubit transmission rate. In the discussion below, errors in the quantum signals due to system drifts or perturbations (as opposed to errors introduced by an eavesdropper) are referred to generally as “system visibility glitches.” System visibility glitches are undesirable because create a transient degradation of system visibility, which generally increases the QBER. 
         [0017]    As described in detail below, an aspect of the present invention involves preventing qubits that are coincident with system visibility glitches greater than a decision threshold value from being included in the raw quantum key. 
       Phase-Encoding QKD System 
       [0018]    An example embodiment of the present invention is now described in connection with a phase-based QKD system  10  as illustrated in  FIG. 2 . As mentioned above and as will be apparent to one skilled in the art, the present invention applies to any actively compensated QKD system, irrespective of the nature of the quantum signal encoding scheme. 
       Alice 
       [0019]    With reference to  FIG. 2 , Alice includes a “quantum light source”  20  adapted to generate quantum signals QS of wavelength λ QS . In one example embodiment, quantum light source  20  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 ). Alice also includes a “classical light source”  30  adapted to generate classical (i.e., multi-photon) signals CS of wavelength λ CS . Classical signals CS are to be used as feedback signals for compensating the shared interferometer, as discussed below. 
         [0020]    Alice further includes a wavelength division multiplexer (WDM)  50 A optically coupled to quantum light source  20  and to classical light source  30  at respective input ports  51 A and  52 A. WDM  50 A also includes an output port  53 A that is optically coupled to an interferometer  60 A at its input port  62 A. Interferometer  60 A also includes an output port  64 A. Interferometer  60 A further includes a modulator MA (e.g., a phase modulator) adapted to impart a randomly selected phase to the quantum signal QS as part of the QKD process. Interferometer  60 A has associated therewith a first differential optical path length OPL A  that can change due to environmental effects at Alice. Interferometer output port is optically coupled to one end of optical fiber link FL. Alice also includes a controller CA that is electrically coupled to modulator MA, quantum light source QS and classical light source CS (and variable optical attenuator  24  if such is present). 
       Bob 
       [0021]    Bob includes an interferometer  60 B that includes an input port  62 B and an output port  64 B. Alice&#39;s interferometer  60 A and Bob&#39;s interferometer  60 B are, strictly speaking, each interferometer halves and together constitute a “shared interferometer.” Interferometer  60 B includes a modulator MB (e.g., a phase modulator) adapted to impart a randomly selected phase to the quantum signal QS as part of the QKD process. 
         [0022]    Interferometer  60 B also has an associated differential optical path length OPL B  that is, in principle, equal to OPL A  to ensure ideal interference of quantum signals. However, OPL A  and OPL B  vary independently as a function of the different environmental effects at Alice and Bob. Accordingly, Bob also includes an adjustable phase/delay element  100  responsive to a feedback signal S F  and adapted to change OPL B  as discussed below. 
         [0023]    Bob also includes a WDM  50 B that includes an input port  53 B and output ports  51 B and  52 B for quantum signals QS and classical signals CS, respectively. Output port  51 B is optically coupled to a single-photon detector (SPD) unit  110 , while output port  52 B is optically coupled to a classical photodetector  120  (e.g., a photodiode). In another embodiment, Bob&#39;s interferometer  60 B has more than one output  64 B and requires a separate WDM  50 B, SPD unit  110 , and classical detector  120  for each output. 
         [0024]    SPD unit  110  is electrically connected to a memory unit  130  included in Bob&#39;s controller CB. Controller CB also includes a feedback processing unit  140 , as well as 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 the SPD unit  10 , etc.). 
         [0025]    Controller CB includes a signal-blanking unit  150  arranged between SPD unit  110  and memory unit  130 . Signal-blanking unit  150  is operably coupled to feedback processing unit  140  and is adapted to receive therefrom a blanking signal S B , as described below. In an example embodiment, signal-blanking unit  150  is or otherwise includes an AND gate  151  that receives an asserted low blanking signal S B  and an asserted high SPD signal S SPD . In normal operation the blanking signal is cleared (logical “1”) and all SPD clicks (logical “1”) pass through AND gate  151  and are stored in memory unit  130 . During a system visibility glitch the blanking signal (logical “0”) prevents the transmission of the SPD signal through AND gate  151 , writing a logical “0” to memory unit  130  to trick it into thinking that the SPD did not fire. 
         [0026]    Controller CB is also electrically coupled to interferometer  50 B, to modulator MB, and to error-adjusting element  100 , which in a phase-based QKD system is or includes an OPL/phase-adjusting element. Controller CB is also operably coupled to Alice&#39;s controller CA so that the overall system timing is coordinated. This is illustrated schematically by a synchronization link SL between the controllers that carries synchronization signals Ss. This synchronization link, however, can be established via optical fiber link FL. 
         [0000]    QKD System Operation with Signal Blanking 
         [0027]    System  10  operates as follows. Alice sends control signals S 20  and S 30  to quantum light source  20  and classical light source  30 , respectively, to cause these light sources to generate respective quantum signals QS and classical signals CS. Quantum and classical signals QS and CS enter WDM  50 A at respective input ports  51 A and  52 A and are multiplexed by the WDM and outputted at output port  53 A. There is a time-delay between the two signals so that they do not overlap. The quantum and classical signals QS and CS enter interferometer  60 A at input port  62 A, wherein the quantum signal is modulated by modulator MA via a timed modulator activation signal SA from controller CA. The time-delay between quantum signal QS and classical signal CS is such that the classical signal passes through the modulator unmodulated (i.e., this signal lies outside of the gating interval provided by modulator activation signal S A ). Quantum signal QS thus becomes a once-modulated quantum signal QS′. 
         [0028]    Classical signal CS and once-modulated quantum signal QS′ exit interferometer  60 A at output port  64 B and are optically coupled onto optical fiber link FL, which carries the signals over to Bob. The signals enter Bob&#39;s interferometer  60 B at input port  62 B. Once-modulated quantum signal QS′ is modulated by modulator MB via a corresponding timed modulator activation signal S B  provided by controller CB, thereby forming a twice-modulated quantum signal QS″. Again, the time-delay between classical signal CS and once-modulated quantum signal QS′ leaves the classical signal unmodulated. Twice-modulated quantum signal QS″ and classical signal CS exit interferometer  60 B at output port  64 B and travel to WDM  50 B. The twice-modulated quantum signal QS″ and the classical signal CS enter WDM  50 B at input port  53 B, are de-multiplexed by the WDM, and are respectively outputted at quantum signal output port  51 B and classical signal output port  52 B. 
         [0029]    The twice-modulated quantum signal QS″ is then detected by SPD unit  110 . SPD unit  110  then generates an SPD signal S SPD  representative of the overall phase modulation (plus the interferometer phase error) imparted to the original quantum signal QS by modulator MA at Alice and modulator MB at Bob. This information is then stored in memory unit  130 . Meanwhile, classical signal CS, with only the phase error φ E  imparted upon it, is detected by photodetector  120 , which in an example embodiment generates a corresponding “error signal” S E  representative of a transient degradation in system visibility. Error signal S E  is provided to feedback processing unit  140  in controller CB. 
         [0030]    Feedback processing unit  140  receives error signal S E  and processes it to produce an appropriate feedback signal S F  to adjustable phase/delay element  100  to change the value of OPL B  to eliminate any phase error. In doing so, adjustable phase/delay element  100  may need to be reset to an operating point near the center of its range of operation. In this case, it is reset to the middle of its range using a re-set signal S R  from feedback processing unit  140 . 
         [0031]    When φ E  and thus S E  are large (thereby requiring a “large” feedback signal S F ), it indicates an imbalance between interferometers  60 A and  60 B. SPD signals S SPD  obtained when the system is in an unbalanced state have a higher probability of increasing the quantum-bit error rate (QBER) since they are more likely to represent “bad” measurements. Errors in the raw quantum key cause a non-linear reduction in the length of the final secure quantum key because of non-linear error-correction and privacy amplification protocols used to obtain a perfectly symmetric quantum key (at least to within a tolerable error). Said differently, such errors reduce the key transmission rate since more quantum signals are needed to establish a quantum key of a given length. 
         [0032]    The measurement of S E  represents a measurement of the phase error φ E , which is superimposed onto the quantum signal bits along with the phases applied by MA and MB. The present invention reduces the QBER by preventing (“blanking”) certain SPD signals S SPD  associated with a large superimposed phase error φ E  from being stored in memory unit  130  and being used in forming the shared quantum key. The blanking is accomplished by feedback processing unit  140  providing one or more blanking signals S B  to memory unit  130  that blanks (prevents) certain SPD signals S SPD  (and thus qubits) from being stored in memory. The generation of blanking signals S B  is based on the value of S E , which represents uncertainty as to the phase state of the quantum pulse(s). 
         [0033]    In an example embodiment, a tolerable phase error threshold φ TH  is set, which corresponds to a tolerable phase error signal threshold S TH . Thus, certain qubits represent “below threshold” qubits for which S E ≦S TH  and which are stored in memory unit  130 , while certain qubits represent “above threshold” qubits for which S E &gt;S TH . The above-threshold qubits are blocked from being stored in memory unit  130  via blocking signals S B . 
         [0034]    In an example embodiment as discussed above, this is accomplished by signal-blanking unit  150  that is or includes AND gate  151  arranged between SPD unit  110  and memory unit  130 . Blocking signals (logical zero) S B  is provided to AND gate  151  to prevent the flow of SPD signals from SPD unit  110  to memory unit  130  for any above-threshold qubits. In another example embodiment, all qubits are stored in an initial raw-bits buffer B 1  in memory unit  130 , and blocking signals are used to identify which qubits should be forwarded to a secondary raw-bits buffer B 2  in memory unit  130  that only includes below-threshold qubits. 
         [0035]    By storing only below-threshold qubits in memory unit  130 , fewer errors are introduced into the raw quantum key. This, in turn, leads to fewer errors in the final quantum key, which is formed by sifting, error-correcting and privacy amplifying the raw key. It also leads to a longer final quantum key for a given number of exchanged qubits because the errors are reduced upfront in the raw key rather than through the aforementioned downstream processing. 
         [0036]    The above description presents a binary approach for the processing of S E , appropriate for implementation through digital hardware. Another approach may be performed in software by adapting the error correction and privacy amplification protocols. 
         [0037]    The typical error correction protocols do not assume any knowledge of which bits have errors. Consequently, the algorithm searches all the bits for errors. Possibly some of the secret bits are revealed as a result of this protocol resulting in their loss. The more errors are present, the more bits are lost. By using S E  to assign a bit-error probability to each bit, erroneous bits can be located while revealing less information and/or without having to search all of the bits. 
         [0038]    This idea may be extended to the privacy amplification process as well. Normally all errors are associated with tampering caused by Eve. The compression ratio, or reduction of secure bits, used in the privacy amplification protocol is usually based on the measured QBER, meaning that higher QBER lead to a greater reduction in the final key rate. However, it is possible to associate a bit-error probability based upon measured values of S E . In an example embodiment, this forms the basis for a new privacy amplification algorithm that adjusts the compression ratio by separating the errors caused by phase errors induced by environmental disturbances at the interferometers from those created by other unknown sources (i.e., Eve). 
         [0039]    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.