Simultaneous classical and quantum communication scheme based on coherent detection
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.
1. A method for coherent optical communications between a sender and a receiver, the method comprising:
selecting, at the sender, two random numbers {x A , p A };
encoding, at the sender, bit m A and {x A , p A } on a coherent state being sent through an optical channel to the receiver, wherein encoding bit m 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 B using the sign of a measured quadrature value {x R , or p R };
displacing, at the receiver, the measured quadrature value {x R , or p R } based on the value of m B to achieve displaced values {x B , or p B } of the corresponding quadrature X or P according to x B =x R +2m B −1 or p B =p R +2m B −1, 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 A , x B } or {p A , p B } into a secret key.
2. The method according to claim 1 wherein the bit m 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 B includes assigning a binary value based on whether the measured quadrature value {x R , or p 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 A , x B } or {p A , p 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 A , x B } or {p A , p 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 A , p A };
encoding, at the sender, a bit m A and random numbers {x A , p A } on a coherent state being sent through an optical channel to the receiver as an optical pulse, wherein encoding bit m 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 B using the sign of a measured quadrature values {x R , p R };
displacing, at the receiver, the measured quadrature values {x R , p R } based on the value of the bit m B to achieve displaced values {x B , p B } of the corresponding X quadrature and P quadrature according to x B =x R +2m B −1 and p B =p R +2m B −1, respectively; and
converting, at the receiver and at the sender, the corresponding quadrature values {x A , x B } and {p A , p B } into a secret key.
8. The method according to claim 7 wherein the random numbers {x A , p 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 A and Gaussian-distributed random numbers {x A , p 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 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 B to achieve a corresponding quadrature value {x B , p B } in accordance with
x
B
=
x
R
T
ch
η
+
(
2
m
B
-
1
)
α
and
P
B
=
P
R
T
ch
η
+
(
2
m
B
-
1
)
α
,
wherein α is an amplitude of the optical pulse and T ch η 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 A , p 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.