Simultaneous classical and quantum communication scheme based on coherent detection

Abstract

An improved coherent communication scheme is provided. The coherent communication scheme encodes both classical and quantum information simultaneously using isolated groups of states: classical information is represented by different groups and can be decoded deterministically; and quantum information is represented by highly overlapped states within the same group, thus guaranteeing security. Decoding includes projecting the detection results at the receiver to one of the distinguishable encoding groups first, which allows the classical information to be read out, and then generating a quantum key from the residual randomness. This communications scheme enables simultaneous classical communication and QKD over the same communication channel using the same transmitter and receiver, opening the door to operate QKD in the background of classical communication and at negligible costs.

Claims

1. A method for coherent optical communications between a sender and a receiver, the method comprising: selecting, at the sender, two random numbers {x.sub.A, p.sub.A}; encoding, at the sender, bit m.sub.A and {x.sub.A, p.sub.A} on a coherent state being sent through an optical channel to the receiver, wherein encoding bit m.sub.A on a coherent state comprises phase-shift keying modulation of an optical pulse; randomly choosing, at the receiver, to measure quadrature X or P with a homodyne detector; determining, at the receiver, bit m.sub.B using the sign of a measured quadrature value {x.sub.R, or p.sub.R}; displacing, at the receiver, the measured quadrature value {x.sub.R, or p.sub.R} based on the value of m.sub.B to achieve displaced values {x.sub.B, or p.sub.B} of the corresponding quadrature X or P according to x.sub.B=x.sub.R+2m.sub.B1 or p.sub.B=p.sub.R+2m.sub.B1, respectively; and informing the sender of the quadrature X or P that was measured, and converting, at the receiver and at the sender, the corresponding quadrature values {x.sub.A, x.sub.B} or {p.sub.A, p.sub.B} into a secret key.

2. The method according to claim 1 wherein the bit m.sub.A is encoded in the X or P quadrature of the optical pulse.

3. The method according to claim 1 wherein determining the bit m.sub.B includes assigning a binary value based on whether the measured quadrature value {x.sub.R, or p.sub.R} is positive or negative.

4. The method according to claim 1 further including sending, from the sender, using a laser diode, a coherent state through the optical channel to the receiver.

5. The method according to claim 1 wherein converting the corresponding quadrature values {x.sub.A, x.sub.B} or {p.sub.A, p.sub.B} into a secret key comprises a reconciliation protocol and a privacy amplification protocol.

6. The method according to claim 1 wherein converting the corresponding quadrature values {x.sub.A, x.sub.B} or {p.sub.A, p.sub.B} into a secret key comprises performing a Gaussian-modulated coherent states quantum key distribution protocol.

7. A method for coherent optical communications between a sender and a receiver, the method comprising: selecting, at the sender, two random numbers {x.sub.A, p.sub.A}; encoding, at the sender, a bit m.sub.A and random numbers {x.sub.A, p.sub.A} on a coherent state being sent through an optical channel to the receiver as an optical pulse, wherein encoding bit m.sub.A on a coherent state comprises phase-shift keying modulation of an optical pulse; measuring, at the receiver with a heterodyne detector, the X quadrature and the P quadrature of the optical pulse; determining, at the receiver, the bit m.sub.B using the sign of a measured quadrature values {x.sub.R, p.sub.R}; displacing, at the receiver, the measured quadrature values {x.sub.R, p.sub.R} based on the value of the bit m.sub.B to achieve displaced values {x.sub.B, p.sub.B} of the corresponding X quadrature and P quadrature according to x.sub.B=x.sub.R+2m.sub.B1 and p.sub.B=p.sub.R+2m.sub.B1, respectively; and converting, at the receiver and at the sender, the corresponding quadrature values {x.sub.A, x.sub.B} and {p.sub.A, p.sub.B} into a secret key.

8. The method according to claim 7 wherein the random numbers {x.sub.A, p.sub.A} are selected from a Gaussian distribution.

9. A method for coherent optical communications comprising: transmitting an optical pulse from a laser light source, the optical pulse carrying phase-encoded binary information based on bit m.sub.A and Gaussian-distributed random numbers {x.sub.A, p.sub.A}; detecting the optical pulse at an optical coherent receiver, the laser light source and the optical coherent receiver being coupled through an optical channel; decoding the phase-encoded binary information from the optical pulse by performing optical homodyne detection or optical heterodyne detection; and generating a quantum key by: measuring at least one quadrature value of the optical pulse, determining bit m.sub.B using the sign of the measured quadrature value, and displacing and resealing the measured quadrature value of the optical pulse using the determined bit m.sub.B to achieve a corresponding quadrature value {x.sub.B, p.sub.B} in accordance with $x_B=\frac{x_R}{\sqrt{T_{\mathrm{ch}}}}+\left(2m_B-1\right)$ and $P_B=\frac{P_R}{\sqrt{T_{\mathrm{ch}}}}+\left(2m_B-1\right),$ wherein is an amplitude of the optical pulse and T.sub.ch is an overall transmittance.

10. The method according to claim 9 wherein generating the quantum key includes performing a reconciliation and privacy amplification protocol.

11. The method according to claim 9 wherein: the phase-encoded binary information is encoded in the X or P quadrature of the optical pulse, and heterodyne detection is used to measure the X and P quadrature of the optical pulse at the optical coherent receiver.

12. The method according to claim 9 wherein the phase-encoded binary information is encoded in the X and P quadrature of the optical pulse.

13. The method according to claim 12 wherein homodyne detection is used to measure the X or P quadrature of the optical pulse at the optical coherent receiver.

14. The method according to claim 9 wherein the Gaussian-distributed random numbers are encoded on two conjugate quadratures of the optical pulse.

15. The method according to claim 9 wherein the Gaussian-distributed random numbers include two random numbers {x.sub.A, p.sub.A} from a Gaussian distribution.

16. The method according to claim 9 wherein the laser light source includes a laser diode and wherein the optical coherent receiver includes a homodyne detector or a heterodyne detector.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a phase space representation of the BPSK modulation scheme.

(2) FIG. 2 is a phase space representation of the GMCS QKD modulation scheme.

(3) FIG. 3 is a phase space representation of the simultaneous BPSK and GMCS QKD modulation scheme in accordance with an embodiment of the present invention.

(4) FIG. 4 is a flow chart illustrating the simultaneous BPSK and GMCS QKD modulation scheme of the current embodiment.

(5) FIG. 5 is a graph illustrating simulation results for the simultaneous BPSK and GMCS QKD modulation scheme of the current embodiment.

DETAILED DESCRIPTION OF THE CURRENT EMBODIMENT

(6) The current embodiment includes a hybrid communications scheme in which classical information is encoded in the displacement of QKD signals. This communications scheme enables simultaneous classical communication and QKD over the same communication channel using the same transmitter and receiver, thereby overcoming the implementation costs of QKD. The current embodiment includes BPSK and GMCS QKD, however other communication protocols can be used in other embodiments, including for example quadrature phase-shift keying (QPSK). BPSK and GMCS QKD are briefly discussed below.

(7) In a BPSK modulation scheme, classical binary information is encoded on the phase of a coherent state and is decoded by performing optical homodyne detection. More specifically, the classic bit value m.sub.A (m.sub.A=0, 1) is encoded by the optical phase (=0, ) as shown in FIG. 1. The probability density function (PDF) of the measurement result X in BPSK is also shown in FIG. 1 (at right). The receiver can decode binary information using the sign of X, e.g., if X>0 (<0), the bit value is assigned as 0 (1). The bit error rate (BER) of the BPSK scheme is determined by the measurement error variance and the signal amplitude. Given the homodyne detector is shot-noise limited (the technical noise is much lower than the vacuum noise), the required signal amplitude for a BER of 10.sup.9 is about 9 photons at the receiver's end.

(8) In a GMCS QKD modulation scheme, Gaussian distributed random numbers are encoded on two conjugate quadratures (X and P) of weak laser pulses, as shown in FIG. 2. After quantum transmission, the sender and the receiver share some correlated data. More particularly, the receiver can perform either optical homodyne detection to measure a randomly chosen quadrature or perform optical heterodyne detection to measure both quadratures simultaneously. After quantum transmission, the receiver announces which quadrature is measured for each incoming signal through an authenticated classical channel, and the sender keeps only the corresponding data. If the observed noise is below a certain threshold, they can further work out a secret key by performing reconciliation and privacy amplification.

(9) In the current embodiment, the above two modulation schemes are combined together. The sender encodes both the classical bit m.sub.A and the Gaussian distributed random numbers (x.sub.A, p.sub.A) (or random number from a non-Gaussian distribution) on the same laser pulse, shown in FIG. 3. In GMCS QKD based on homodyne detection, the receiver measures either X or P quadrature of each incoming signal. To achieve deterministic classical communication, the same classical bit m.sub.A can be encoded on both X and P quadrature. If heterodyne detection is employed, the sender only needs to encode m.sub.A on one quadrature. From the measurement result x.sub.R (or p.sub.R), the receiver can decode classical bit m.sub.B using the sign of x.sub.R (or p.sub.R), e.g., if x.sub.R (or p.sub.R)>0, then the value of m.sub.B is assigned as 0. Otherwise, the value of m.sub.B is assigned as 1. To further generate the secure key, the receiver displaces and rescales the measurement result based on the value of m.sub.B as:
x.sub.B=x.sub.R+2m.sub.B1(1)
p.sub.B=p.sub.R+2m.sub.B1(2)

(10) The sender and the receiver can work out a secret key from {x.sub.A; x.sub.B} and {p.sub.A; p.sub.B}, just as in the case of conventional GMCS QKD. Essentially, the states prepared by the sender are displaced Gaussian modulated coherent states, where the amount of the displacement is determined by the classical bit m.sub.A. Given a modulation variance of the Gaussian random numbers, the BER of classical communication can be reduced effectively by using a large displacement.

(11) Referring now to FIG. 4, a flow chart illustrating a method for simultaneous classical communication and QKD protocol in accordance with one embodiment is presented. In general terms, the method can include the following steps: (a) transmitting an optical pulse from a laser light source, the optical pulse carrying phase-encoded binary information and Gaussian-distributed random numbers; (b) detecting the optical pulse at an optical coherent receiver; (c) decoding the phase-encoded binary information from the optical pulse; and (d) generating a quantum key by measuring at least one quadrature value of the optical pulse. If only one quadrature is measured, the method further includes informing a sender of the optical pulse of the quadrature that was measured. Each step is discussed below.

(12) Transmitting an optical pulse is depicted as step 10 in FIG. 4. This step generally includes selecting, at the sender, two random numbers {x.sub.A, p.sub.A} from a Gaussian distribution and encoding a classical bit m.sub.A and the random numbers {x.sub.A, p.sub.A} on a coherent state: |(x.sub.A+e.sup.im.sup.A.sup.)+i(p.sub.A+e.sup.im.sup.A.sup.), as shown in FIG. 3. The classical bit m.sub.A is encoded in the X quadrature, P quadrature, or both quadratures of an optical pulse transmitted to the recipient. If both quadratures are encoded, homodyne detection can be used at the recipient. If only one quadrature is encoded, heterodyne detection can be used at the recipient.

(13) Detecting the optical pulse is depicted as step 12 in FIG. 4. This step generally includes detecting the optical pulse at an optical coherent receiver that is coupled to a laser light source (e.g., a laser diode) of the sender via an optical channel. If homodyne detection scheme is chosen, this step additionally includes randomly choosing, at the receiver, to measure quadrature X or quadrature P in accordance with the GMCS QKD protocol to obtain {x.sub.R, p.sub.R}.

(14) Decoding the phase-encoded binary information from the optical pulse is depicted at step 14 in FIG. 4. This step generally includes determining, at the receiver, bit m.sub.B using the sign of a measured quadrature value {x.sub.R, p.sub.R}. If the receiver measured the X quadrature, the measurement result is x.sub.R. If the receiver measured the P quadrature, the measurement result is p.sub.R. Determining the bit m.sub.B includes assigning a binary value based on whether the measured quadrature value {x.sub.R, p.sub.R} is positive or negative. For example, if x.sub.R is >0, the value of m.sub.B is assigned as 0 but if x.sub.R is <0 the value of m.sub.B is assigned as 1. These values can be reversed, such that if x.sub.R is >0, the value of m.sub.B is assigned as 1 but if x.sub.R is <0 the value of m.sub.B is assigned as 0. Similarly, if p.sub.R is >0, the value of m.sub.B is assigned as 0 (or 1) but if p.sub.R is <0 the value of m.sub.B is assigned as 1 (or 0).

(15) Generating a quantum key is depicted as step 16 in FIG. 4. This step generally includes rescaling and displacing, at the receiver, the measured quadrature value {x.sub.R, p.sub.R} based on the value of m.sub.B. This step can performed according to equations (1) and (2) above, or according to equations (3) and (4) below, based on the signal amplitude and overall transmittance T.sub.ch:

(16) $\begin{array}{cc}{x}_B=\frac{x_R}{\sqrt{T_{\mathrm{ch}}}}+\left(2m_B-1\right)& \left(3\right)\\ p_B=\frac{p_R}{\sqrt{T_{\mathrm{ch}}}}+\left(2m_B-1\right)& \left(4\right)\end{array}$
The resulting Gaussian values {x.sub.B, p.sub.B} can be converted into a secret key in accordance with GMCS QKD. In particular, the recipient can inform the sender of the quadrature that was measured and can perform reconciliation (direct or reverse) and privacy amplification protocols. In direct (reverse) reconciliation, the sender (the recipient) sends additional classical information to the recipient (the sender) to implement error correction and generate an error-free key. In privacy amplification, the above error-free key will be further shortened to remove any information an eavesdropper could have and generate a final secure key.

(17) Numerical simulations of secure key rate at different phase noise variations were performed according to the hybrid communications scheme of the current embodiment. The simulation results are shown in FIG. 5. The performance of the hybrid communications scheme was found to be heavily dependent on the phase noise of the system. The results suggested that simultaneous classical and QKD over tens of kilometers of optical fiber is possible.

(18) The above description is that of current embodiments of the invention. Various alterations and changes can be made without departing from the spirit and broader aspects of the invention as defined in the appended claims, which are to be interpreted in accordance with the principles of patent law including the doctrine of equivalents. This disclosure is presented for illustrative purposes and should not be interpreted as an exhaustive description of all embodiments of the invention or to limit the scope of the claims to the specific elements illustrated or described in connection with these embodiments. The present invention is not limited to only those embodiments that include all of these features or that provide all of the stated benefits, except to the extent otherwise expressly set forth in the issued claims. Any reference to claim elements in the singular, for example, using the articles a, an, the or said, is not to be construed as limiting the element to the singular.