Abstract

A theoretical analysis of two simple implementations for optical receivers that achieve near-quantum optimum performance for phase-quadrature coherent-state signaling is carried out. For a large received average photon count per symbol, Ns, the error probability is proportional to exp(−2Ns) as opposed to the conventional heterodyne performance of exp(−Ns/2).

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976), Chap. VI, p. 187.
  2. R. S. Kennedy, MIT Res. Lab. Electron. Q. Rep. 108, 219–225 (1973).
  3. S. J. Dolinar, MIT Res. Lab. Electron. Q. Rep. 111, 115–120 (1973).
  4. K. Yamazaki, in Quantum Aspects of Optical Communications, C. Bendjaballah, O. Hirotu, S. Reynaud, eds., Vol. 378 of Springer Series of Lecture Notes in Physics (Springer-Verlag, Berlin, 1991), pp. 367–375.
    [CrossRef]
  5. H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
    [CrossRef]
  6. D. Snyder, Random Point Processes (Wiley, New York, 1975), Chap. 2.

1975 (1)

H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
[CrossRef]

1973 (2)

R. S. Kennedy, MIT Res. Lab. Electron. Q. Rep. 108, 219–225 (1973).

S. J. Dolinar, MIT Res. Lab. Electron. Q. Rep. 111, 115–120 (1973).

Dolinar, S. J.

S. J. Dolinar, MIT Res. Lab. Electron. Q. Rep. 111, 115–120 (1973).

Helstrom, C. W.

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976), Chap. VI, p. 187.

Kennedy, R. S.

H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
[CrossRef]

R. S. Kennedy, MIT Res. Lab. Electron. Q. Rep. 108, 219–225 (1973).

Lax, M.

H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
[CrossRef]

Snyder, D.

D. Snyder, Random Point Processes (Wiley, New York, 1975), Chap. 2.

Yamazaki, K.

K. Yamazaki, in Quantum Aspects of Optical Communications, C. Bendjaballah, O. Hirotu, S. Reynaud, eds., Vol. 378 of Springer Series of Lecture Notes in Physics (Springer-Verlag, Berlin, 1991), pp. 367–375.
[CrossRef]

Yuen, H. P.

H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
[CrossRef]

IEEE Trans. Inf. Theory (1)

H. P. Yuen, R. S. Kennedy, M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
[CrossRef]

MIT Res. Lab. Electron. Q. Rep. (2)

R. S. Kennedy, MIT Res. Lab. Electron. Q. Rep. 108, 219–225 (1973).

S. J. Dolinar, MIT Res. Lab. Electron. Q. Rep. 111, 115–120 (1973).

Other (3)

K. Yamazaki, in Quantum Aspects of Optical Communications, C. Bendjaballah, O. Hirotu, S. Reynaud, eds., Vol. 378 of Springer Series of Lecture Notes in Physics (Springer-Verlag, Berlin, 1991), pp. 367–375.
[CrossRef]

D. Snyder, Random Point Processes (Wiley, New York, 1975), Chap. 2.

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976), Chap. VI, p. 187.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Block diagram of the receiver. The output of the ideal photodetector is fed back to an optical phase shifter that applies a phase shift to the locally generated field that is proportional to the received photon count. The local field is combined with the received field with a beam splitter that has near-unity transmission. The receiver tries to null out the received field by incrementing the phase shift every time a photon is detected.

Fig. 2
Fig. 2

Plot of receiver performance, showing the performance in terms of symbol error probability of the quantum optimum QPSK receiver from Ref. 1, the performance of the type I and type II receivers, and the performance of heterodyne QPSK. The horizontal axis is photons per symbol in decibels.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

P ( error ) = 1 / 2 exp ( 2 N s ) ,
E m = N s exp ( j m π 2 ) , m = 0 , 1 , 2 , 3 .
I ( t ) = 2 N s T { 1 cos [ m π 2 N ( t ) π 2 ] } , 0 t T , m = 0 , 1 , 2 , 3
P ( error | m 1 ) = exp ( 2 N s ) .
P ( no counts | m 2 ) = exp ( 4 N s ) ,
P ( only 1 count | m 2 ) = 0 T d t 1 4 N s T exp ( 4 N s t 1 T ) exp [ 2 N s ( T t 1 ) T ] = 2 [ exp ( 2 N s ) exp ( 4 N s ) ] .
P ( error | m 2 ) = 2 exp ( 2 N s ) exp ( 4 N s ) .
P ( no counts | m 3 ) = exp ( 2 N s ) ,
P ( 1 count only | m 3 ) = exp ( 2 N s ) exp ( 4 N s ) ,
= 0 T d t 1 t 1 T d t 2 2 N s T exp ( 2 N s t 1 T ) 4 N s T × exp [ 4 N s ( t 2 t 1 ) T ] exp [ 2 N s ( T t 2 ) T ] = 4 N s exp ( 2 N s ) 2 exp ( 2 N s ) + 2 exp ( 4 N s ) .
P ( error | m 3 ) = 4 N s exp ( 2 N s ) exp ( 4 N s ) .
P ( error ) = exp ( 2 N s ) ( N s + 3 / 4 ) ,
P ( error | m 0 ) = 0 ,
P ( error | m 1 ) = P ( no counts ) = exp ( 2 N s ) .
0 T d t 1 t 1 min 2 t 1 , T d t 2 { 4 N s T exp ( 4 N s t 1 T ) 2 N s T × exp [ 2 N s ( T 2 t 1 ) T ] exp [ 2 N s ( T T 2 ) T ] } .
P ( error | m 2 ) = 4 exp ( 2 N s ) + 4 ( N s 1 ) exp ( 3 N s ) + exp ( 4 N s ) 4 N s exp ( 4 N s ) .
0 T / 2 d t 1 2 t 1 T d t 2 2 N s T exp ( N s t i T ) 4 N s T × exp [ 4 N s ( t 2 t 1 ) T ] exp [ 2 N s ( T t 2 ) T ] = 2 exp ( 2 N s ) 4 exp ( 3 N s ) + 2 exp ( 4 N s ) .
P ( error | m 3 ) = 4 exp ( 2 N s ) 4 exp ( 3 N s ) + exp ( 4 N s ) ,
P ( error ) = 9 4 exp ( 2 N s ) 2 exp ( 3 N s ) + N s exp ( 3 N s ) + 1 2 exp ( 4 N s ) N s exp ( 4 N s ) .

Metrics