Abstract:
A method of distributing a quantum key from a sender to a recipient. The recipient generates a pulse having multiple photons; splits the pulse into first and second sub-pulses; phase modulates the first sub-pulse with a secret key; and transmits both the phase-modulated first sub-pulse and the second sub-pulse to the sender. The sender receives the phase-modulated first sub-pulse and the second sub-pulse from the recipient; encodes a quantum key bit into one of the sub-pulses received from the recipient; and transmits both the phase-modulated first sub-pulse and the second sub-pulse back to the recipient. Then, the recipient receives the phase-modulated first sub-pulse and the second sub-pulse from the sender; phase modulates the second sub-pulse with the secret key; combines the phase-modulated first sub-pulse and the phase-modulated second sub-pulse to produce a composite pulse; and processes the composite pulse in an attempt to detect the quantum key bit.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present application is a CONTINUATION under 35 USC §120 of PCT International Patent Application bearing Serial No. PCT/CA2006/000644, filed on Apr. 24, 2006, and is hereby incorporated by reference; the present application also claims the benefit of priority under 35 USC §119(e) of U.S. Provisional Patent Application Ser. No. 60/872,425, filed on Sep. 30, 2005, and is incorporated herein by reference. 
   The present application claims the benefit under 35 USC §120, and is a CONTINUATION-IN-PART, of U.S. patent application Ser. No. 11/241,164 to Kuang et al., filed on Sep. 30, 2005, hereby incorporated by reference herein. 

   FIELD OF THE INVENTION 
   This invention relates generally to the field of network communications, and more particularly to communications over a quantum channel. 
   BACKGROUND 
   Public key encryption is currently a popular technique for secure network communications. Public key encryption utilizes “one-way functions” that are relatively simple for computers to calculate, but difficult to reverse calculate. In particular, a one way function ƒ(x) is relatively easy for a computer to calculate given the variable x, but calculating x given ƒ(x) is difficult for the computer, although not necessarily impossible. Some one way functions can be much more easily reverse calculated with the assistance of particular “trap door” information, i.e., a key. Public key cryptography utilizes such one-way functions in a two-key system in which one key is used for encryption and the other key is used for decryption. In particular, the one-way function is a “public key” which is openly advertised by Node A for the purposes of sending encrypted messages to Node A. The trap door key is a “private key” which is held in confidence by Node A for decrypting the messages sent to Node A. For two-way encrypted communications each node utilizes a different public key and a different private key. One advantage of this system is that secure key distribution is not required. However, advances in the capabilities of computers tend to erode the level of security provided by public key encryption because the difficulty of reverse calculating the one-way function decreases as computing capabilities increase. 
   It is generally accepted in the field of cryptology that the most secure encryption technique is the Vernam cipher, i.e., one-time pad. A Vernam cipher employs a key to encrypt a message that the intended recipient decrypts with an identical key. The encrypted message is secure provided that the key is random, at least equal to the message in length, used for only a single message, and known only to the sender and intended receiver. However, in modern communication networks the distribution of Vernam cipher keys is often impractical, e.g., because the keys can be quite long and key distribution itself is subject to eavesdropping. 
   One technique for secure key distribution is known as Quantum Key Distribution (“QKD”). Quantum Key Distribution transmits an individual photon for each bit of the key being distributed to an intended recipient. The photons may be polarization modulated in order to differentiate logic 1 from logic 0. Distribution of the quantum key is secure because of the laws of quantum physics. In particular, it is not possible to measure an unknown quantum state of a photon without modifying it. Hence, an eavesdropper attempting to intercept the key would introduce detectable errors into the key. Unfortunately, photon-per-bit key distribution is so inefficient with current technology as to be impractical. This is due in-part to the attenuation technique and equipment used to generate a single photon pulse. In particular, in order to avoid transmitting more than one photon the attenuator must be set such that about 91% of the attempted pulses generate zero photons. 
   SUMMARY OF THE INVENTION 
   In accordance with a first broad aspect, the present invention seeks to provide a method of distributing a quantum key between a first node and a second node. The method comprises, by the second node: generating a pulse having multiple photons; splitting the pulse into first and second sub-pulses; phase modulating the first sub-pulse with a secret key; and transmitting both the phase-modulated first sub-pulse and the second sub-pulse to the first node. The method further comprises, by the first node: receiving the phase-modulated first sub-pulse and the second sub-pulse from the second node; encoding a quantum key bit into one of the sub-pulses received from the second node; and transmitting both the phase-modulated first sub-pulse and the second sub-pulse back to the second node. Then, the method further comprises, by the second node: receiving the phase-modulated first sub-pulse and the second sub-pulse from the first node; phase modulating the second sub-pulse with the secret key; processing the phase-modulated first sub-pulse and the phase-modulated second sub-pulse in an attempt to detect the quantum key bit. 
   In accordance with a second broad aspect, the present invention seeks to provide a method of participating in distribution of a quantum key with a first node. The method comprises generating a pulse having multiple photons; splitting the pulse into first and second sub-pulses; phase modulating the first sub-pulse with a secret key; transmitting both the phase-modulated first sub-pulse and the second sub-pulse to the first node; receiving the phase-modulated first sub-pulse and the second sub-pulse from the first node, one of the phase-modulated first sub-pulse and the second sub-pulse having been encoded with a quantum key bit; phase modulating the second sub-pulse with the secret key; processing the phase-modulated first sub-pulse and the phase-modulated second sub-pulse in an attempt to detect the quantum key bit. 
   In accordance with a third broad aspect, the present invention seeks to provide an apparatus, which comprises means for generating a pulse having multiple photons; means for splitting the pulse into first and second sub-pulses; means for phase modulating the first sub-pulse with a secret key; means for transmitting both the phase-modulated first sub-pulse and the second sub-pulse to a node; means for receiving the phase-modulated first sub-pulse and the second sub-pulse from the node, one of the phase-modulated first sub-pulse and the second sub-pulse having been encoded with a quantum key bit; means for phase modulating the second sub-pulse with the secret key; means for processing the phase-modulated first sub-pulse and the phase-modulated second sub-pulse in an attempt to detect the quantum key bit. 
   In accordance with a fourth broad aspect, the present invention seeks to provide a node operable to receive a quantum key. The node comprises a photon source operable to generate a pulse having multiple photons; a coupler operable to split the pulse into first and second sub-pulses, the first sub-pulse being sent along a first loop and the second sub-pulse being sent along a second loop shorter than the first loop; a phase modulator in the first loop operable to phase modulate the first sub-pulse with a secret key; a port operable to transmit both the phase-modulated first sub-pulse and the second sub-pulse to an other node, the other node being operable to encode at least one of the phase-modulated sub-pulse and the second sub-pulse with a quantum key bit. The port is further operable to receive the phase-modulated first sub-pulse and the second sub-pulse from the other node. The node further comprises a polarization beam splitter operable to send the received phase-modulated first sub-pulse along the second loop and the received second sub-pulse along the first loop. The phase modulator is further operable to phase modulate the received second sub-pulse with the secret key. The coupler is further operable to combine the received phase-modulated first sub-pulse and the phase-modulated received second sub-pulse to produce a composite pulse. The second node further comprises a detection unit operable to process the composite pulse in an attempt to detect the quantum key bit. 
   It will thus be appreciated by persons skilled in the art that quantum key distribution in accordance with certain embodiments of the invention enables use of multi-photon pulses without unacceptable loss of security, thereby enhancing the bit rate with which a quantum key can be distributed securely. 
   These and other aspects and features of the present invention will now become apparent to those of ordinary skill in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
       FIG. 1  is a block diagram illustrating travel of a first sub-pulse from a second node “Bob” to a first node “Alice” and back to Bob; 
       FIG. 2  is a block diagram illustrating travel of a second sub-pulse from Bob to Alice and back to Bob. 
   

   It is to be expressly understood that the description and drawings are only for the purpose of illustration of certain embodiments of the invention and are an aid for understanding. They are not intended to be a definition of the limits of the invention. 
   DETAILED DESCRIPTION OF EMBODIMENTS 
     FIGS. 1 and 2  illustrate a first node  100  (also referred to as “Alice”) and a second node  102  (also referred to as “Bob”) of a communications network. Alice  100  and Bob  102  employ double phase encoding quantum key distribution (“QKD”). Alice  100 , the sender of a quantum key having a plurality of quantum key bits, includes a phase modulator PMa  104  and a Faraday Mirror  106 . Bob  102 , the recipient of the quantum key, includes an attenuator  108 , phase modulator PMb  110 , phase modulator PMs  112 , Polarization Beam Splitter (PBS)  114 , a coupler (and/or beamsplitter)  116 , a photon source  118  (e.g., a laser diode), and a detection unit (including a detector  120  triggered by a pulse affected with constructive interference and a detector  122  triggered by a pulse affected with destructive interference). 
   A series of short laser pulses is employed for quantum key distribution between Alice  100  and Bob  102 . The short laser pulses are generated by the laser diode  118  at Bob  102 . Considering now the case of a single pulse from the laser diode  118 , coupler  116  splits the pulse into two pulses, hereinafter referred to as “P 1 ” and “P 2 ”. Pulse P 1  (shown in  FIG. 1 ) is transmitted via a “long” loop and pulse P 2  (shown partly in  FIG. 1  but primarily in  FIG. 2 ) is transmitted via a “short” loop. 
   Referring now to only  FIG. 1 , the phase modulator PMs  112  modulates a randomly-selected secret phase key Φs into the pulse P 1  travelling in the long loop. The secret phase key Φs is unknown to Alice  100  and is used only by Bob  102 . The secret phase key Φs can be randomly generated. The secret phase key is used to identify whether the pulses sent by Alice  100  really were based on pulses sent by Bob  102 , i.e., whether the instant distribution of the quantum key has been attacked by an eavesdropper. It may be desirable that the secret phase key Φs differ from phase sequences modulated by phase modulators PMa  104  and PMb  110  (which in an embodiment are selected from quantum encoding bases B 1  (having elements 0 and π) and B 2  (having elements π/2 and 3π/2)). It is noted that Bob&#39;s phase modulator PMb  110  in the long loop is inactive at this time. 
   When pulse P 1  arrives at PBS  114  (with phase Φs), the horizontal polarization of pulse P 1  is reflected by to the attenuator  108 . The attenuator  108  reduces the average photon number in pulse P 1  to a selected level which is greater than one, so as to increase the likelihood of efficient, successful transmission, but not so large as to enable easy eavesdropping, e.g., μ=10. After suitable attenuation the pulse P 1  is fed to a quantum channel (Q-channel) such as an optical fiber. 
   Alice  100  is operable to receive pulse P 1  from the quantum channel and enable phase modulator PMa  104  to modulate the pulse P 1  with a phase shift ø 1  associated with a given quantum key bit. The phase shift ø 1  will have a value that is characterized by a quantum encoding basis and a polarity. The choice of quantum encoding basis (i.e., B 1  or B 2 ) is random and is known only to Alice  100 . Having selected which quantum encoding basis to use, for example B 1  (where the possible phases are 0 and π), then the polarity (i.e., whether the phase shift ø 1  will be 0 or π in the case of B 1  or whether the phase shift ø 1  will be π/2 or 3π/2 in the case of B 2 ) depends on the value of the given quantum key bit that Alice  100  is transmitting. After having passed through the phase modulator PMa  104 , pulse P 1  will have a phase shift of Φs+ø 1 . 
   Next, pulse P 1  arrives at the Faraday mirror  106 , which reflects pulse P 1  back and flips its polarization, i.e., causes a change of π/2 in the phase. The resulting pulse, which now has a phase shift of (Φs+ø 1 +π/2) and is denoted P 1 ′, is then transmitted back to Bob  102 . 
   Bob  102  is operable to receive returning pulse P 1 ′ from Alice  100 . The PBS  114  is operable to direct returning pulse P 1 ′ into the “short” loop due to the polarization flip by Alice&#39;s Faraday mirror  106 . Returning pulse P 1 ′ then arrives at the coupler  116 , where it is combined with a returned version of pulse P 2 , which will now be described. 
   Specifically, referring to  FIG. 2 , after being generated at Bob&#39;s coupler  116 , pulse P 2  takes the “short” loop. Upon arrival at the PBS  114 , the PBS  114  transmits the vertical polarization of P 2  towards the attenuator  108 , where pulse P 2  is subjected to the same attenuation as pulse P 1 , e.g., μ=10. Pulse P 2  travels over the quantum channel as was described above with regard to pulse P 1 . 
   Alice  100  is then operable to receive pulse P 2  from the quantum channel. Following receipt of pulse P 2 , Alice  100  is operable to flip the polarization of pulse P 2  at Faraday mirror  106  (i.e., causes a change of π/2 in the phase). The reflected pulse, which now has a phase shift of π/2 and is denoted P 2 ′, is then sent back onto the quantum channel. It is noted that Alice&#39;s phase modulator PMa  104  is inactive at this time. 
   Bob  102  is operable to receive returning pulse P 2 ′ from Alice  100 . Returning pulse P 2 ′ is directed into the long loop at the PBS  114  due its polarization flip at the Faraday mirror  106 . On the long loop, Bob&#39;s phase modulator PMb  110  modulates a phase shift ø 2  onto returning pulse P 2 ′. The phase shift ø 2  is characterized by a quantum encoding basis and a polarity. The quantum encoding basis is selected randomly from B 1  and B 2 . As for the polarity, it can always be the same or it can vary, as long as Bob  102  remembers both the quantum encoding basis and the polarity used to modulate a given returning pulse P 2 ′. In addition, phase modulator PMs then modulates returning pulse P 2 ′ with the same secret phase key Φs that was used to modulate pulse P 1 . Thus, returning pulse P 2 ′ now has a phase of (Φs+ø 2 +π/2). 
   Referring again to both  FIGS. 1 and 2 , returning pulses P 1 ′ and P 2 ′ arrive at Bob&#39;s coupler  116  at the same time because both pulses have traversed the same overall round-trip path, albeit with the loops in different order. Further, both returning pulses P 1 ′ and P 2 ′ will have been modulated with the same secret phase key Φs. Specifically, it is recalled that returning pulse P 1 ′ has a phase shift of (Φs+ø 1 +π/2) and returning pulse P 2 ′ has a phase shift of (Φs+ø 2 +π/2). Thus, the two returning pulses P 1 ′ and P 2 ′ combine at coupler  116  to form a composite pulse having a phase shift of Δø=ø 1 −ø 2 . 
   The detection unit operates on the composite pulse as follows: when the quantum encoding basis used by PMb  110  matches the quantum encoding basis used by PMa  104 , the composite pulse will cause a measurement to be recorded at only one of the detectors (e.g., either detector  120  or detector  122 ). This is known as a “one-click”. Under such circumstances, which of the two detectors  120 ,  122  will record a measurement will depend only on whether the polarity used by PMb  110  matches the polarity used by PMa  104 . Of course, because Bob  102  knows the polarity used by Bob&#39;s own phase modulator PMb  110 , the value of the quantum bit encoded by Alice  100  will be easily derivable by combining this polarity and the identity of the detector  120 ,  122  that records a measurement (which indicates whether ø 2  did or did not happen to match ø 1 ). 
   However, when the quantum encoding basis used by PMb  110  does not match the quantum encoding basis used by PMa  104 , each photon in the composite pulse will be picked up by either detector  120  or detector  122  with approximately equal probability (as the interference is neither strictly constructive nor strictly destructive), which may even result in a measurement being recorded at both of the detectors  120 ,  122 . Under such circumstances, there is no relation between the measurements at the detectors  120 ,  122  and the match or mismatch between the polarity used by Alice&#39;s phase modulator PMa  104  and the polarity used by Bob&#39;s phase modulator PMb  110 . In short, the detection results cannot be relied upon to extract information. 
   It follows from the above that if Bob  102  were to know that the correct quantum encoding basis has been used for a given quantum key bit, then Bob  102  could learn the polarity of the quantum key bit by simply performing an “exclusive or” (XOR) between whatever polarity was used by Bob&#39;s phase modulator PMb  110  and the identity of the detector that recorded a measurement (using “0” for detector  120  and “1” for detector  122 ). Equivalently, if Bob  102  were to know that the correct quantum encoding basis has been used for a given quantum key bit, and if Bob&#39;s phase modulator PMb  110  were to consistently use the same polarity (e.g., 0) irrespective of the quantum encoding basis, then Bob  102  could detect the polarity of the quantum key bit by simply noting which of the two detectors  120 ,  122  recorded a measurement. 
   In order for Bob  102  to obtain the aforesaid knowledge of whether the correct quantum encoding basis was used in the first place, Bob  102  may publicly tell Alice  100  the quantum encoding bases that were used, and Alice  100  can then reply to Bob  102  specifying which are correct. 
   Now, having detected the polarities for a subset of the quantum key bits (i.e., for those instances where the quantum encoding basis used by PMb  110  matches the quantum encoding basis used by PMa  104 ), Bob  102  can determine the corresponding quantum key bits sent by Alice  100 . This subset of quantum key bits can be referred to as a shifted key. Further steps can be performed (such as BB84 error correction and privacy amplification) and the final secret key can be determined. 
   From the above, it will be apparent that a general advantage of certain embodiments of the invention is more efficient and practical distribution of a quantum key having a plurality of quantum bits. Efficiency is enhanced because multiple photons can be used to represent each bit of the quantum key. Using multiple photons enable use of attenuator settings that are less likely to result in zero photons (complete attenuation). 
   Security against an “intercept-and-resend” attack is maintained because attempted eavesdropping can be detected from a phase mismatch being introduced by the attacking party. This gives rise to either (I) both detectors  120 ,  122  recording a measurement even though only one detector is expected to record a measurement; and/or (II) increased quantum bit error rate (QBER). 
   Security against a “photon-split” attack is maintained despite using multiple photons per pulse (where each individual photon in the pulse has 100% of the information of the encoded key bit value) due to the use of the secret phase key Φs, which is modulated by Bob  102  into pulse P 1  on the way out and into returning pulse P 2 ′ upon receipt from Alice  100 . Because of randomization of Φs it cannot be correctly guessed by the attacking party. Specifically, suppose that the attacking party indeed attempts a “photon-split” attack technique, i.e., by splitting a single photon portion p 1  from P 1 ′ and p 2  from P 2 ′ after these pulses have been sent by Alice  100 . (Note that the phase shift of p 1  is (Φs+ø 1 +π/2) and that the phase of p 2  is (ø 2 +π/2) because it has not yet been processed by Bob&#39;s  102  long loop in the return path). The attacking party needs to combine p 1  and p 2  together to create an original photon which carries quantum key information. Also suppose that the attacking party somehow learns the measurement information from communication between Bob  102  and Alice  100  and somehow successfully guesses phase shifts ø 1  and ø 2 . It is noted that the phase difference between p 1  and p 2  will be (ø 1 −ø 2 +Φs). Thus, even if the attacking party knows ø 1  and ø 2 , the attacking party still cannot guess which detector ( 120  or  122 ) would record a measurement because of the attacking party&#39;s lack of knowledge about the secret phase key Φs. Further, the eavesdropping attempts will tend to increase the QBER, which can be detected by Bob  102 . Therefore, the invention is a secure key distribution technique, even for multi-photon pulses. 
   Another advantage of certain embodiments of the invention is that the need for active polarization compensation is obviated. In particular, since the initial pulse is split into two pulses which traverse the same round-trip path there is no need for polarization compensation. Further, the same laser can be employed for both synchronization and key distribution. Other advantages will be apparent in view of the foregoing detailed description. 
   While the invention is described through the above exemplary embodiments, it will be understood by those of ordinary skill in the art that modification to and variation of the illustrated embodiments may be made without departing from the inventive concepts herein disclosed. Moreover, while the preferred embodiments are described in connection with various illustrative structures, one skilled in the art will recognize that the system may be embodied using a variety of specific structures. Accordingly, the invention should not be viewed as limited except by the scope and spirit of the appended claims.