Abstract

A quantum heterodyne-detection system is described that affords K-ary phase-based digital communication at zero error probability at an average photon number of approximately K3/2. In phase-based precision measurement—at the same average photon number—this system can measure an arbitrary c-number phase shift to within ±π/K rad with probability one.

© 1995 Optical Society of America

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References

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  1. W. P. Schleich, S. M. Barnett, eds., special issue on quantum phase and phase dependent measurements, Phys. Scr. T48, 5–142 (1993).
  2. A. Luks, V. Perinová, Quantum Opt. 6, 125 (1994).
    [CrossRef]
  3. J. H. Shapiro, Phys. Scr. T 48, 105 (1993).
    [CrossRef]
  4. J. H. Shapiro, S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
    [CrossRef]
  5. This guaranteed phase precision is accomplished through the use of a two-mode entangled state. Interestingly, C. H. Bennett and S. J. Wiesner have recently proposed entanglement for another error-free quantum communication purpose [Phys. Rev. Lett. 69, 2881 (1992)]. Their motivation is quantum cryptography, however, not quantum phase measurement.
    [PubMed]
  6. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  7. J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh, M. C. Teich, J. Opt. Soc. Am. B 4, 1604 (1987).
    [CrossRef]
  8. G. Saplakoglu, “Photodetection feedback systems,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., July1988).

1994 (1)

A. Luks, V. Perinová, Quantum Opt. 6, 125 (1994).
[CrossRef]

1993 (1)

J. H. Shapiro, Phys. Scr. T 48, 105 (1993).
[CrossRef]

1992 (1)

This guaranteed phase precision is accomplished through the use of a two-mode entangled state. Interestingly, C. H. Bennett and S. J. Wiesner have recently proposed entanglement for another error-free quantum communication purpose [Phys. Rev. Lett. 69, 2881 (1992)]. Their motivation is quantum cryptography, however, not quantum phase measurement.
[PubMed]

1987 (1)

1984 (1)

J. H. Shapiro, S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
[CrossRef]

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Caves, C. M.

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Ho, S.-T.

Kumar, P.

Luks, A.

A. Luks, V. Perinová, Quantum Opt. 6, 125 (1994).
[CrossRef]

Perinová, V.

A. Luks, V. Perinová, Quantum Opt. 6, 125 (1994).
[CrossRef]

Saleh, B. E. A.

Saplakoglu, G.

J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh, M. C. Teich, J. Opt. Soc. Am. B 4, 1604 (1987).
[CrossRef]

G. Saplakoglu, “Photodetection feedback systems,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., July1988).

Shapiro, J. H.

J. H. Shapiro, Phys. Scr. T 48, 105 (1993).
[CrossRef]

J. H. Shapiro, G. Saplakoglu, S.-T. Ho, P. Kumar, B. E. A. Saleh, M. C. Teich, J. Opt. Soc. Am. B 4, 1604 (1987).
[CrossRef]

J. H. Shapiro, S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
[CrossRef]

Teich, M. C.

Wagner, S. S.

J. H. Shapiro, S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. H. Shapiro, S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

This guaranteed phase precision is accomplished through the use of a two-mode entangled state. Interestingly, C. H. Bennett and S. J. Wiesner have recently proposed entanglement for another error-free quantum communication purpose [Phys. Rev. Lett. 69, 2881 (1992)]. Their motivation is quantum cryptography, however, not quantum phase measurement.
[PubMed]

Phys. Scr. T (1)

J. H. Shapiro, Phys. Scr. T 48, 105 (1993).
[CrossRef]

Quantum Opt. (1)

A. Luks, V. Perinová, Quantum Opt. 6, 125 (1994).
[CrossRef]

Other (2)

W. P. Schleich, S. M. Barnett, eds., special issue on quantum phase and phase dependent measurements, Phys. Scr. T48, 5–142 (1993).

G. Saplakoglu, “Photodetection feedback systems,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass., July1988).

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Figures (2)

Fig. 1
Fig. 1

Block diagram of a phase-conjugate quantum communication system with heterodyne detection.

Fig. 2
Fig. 2

Shift-invariant, phase measurement pdf’s, p(ϕ|Φ) = f(ϕ − Φ): the raised-cosine is confined to |ϕ| ≤ π/K, and the Gaussian has the same variance as the raised cosine. K ≫ 1 is assumed.

Equations (17)

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f ( ϕ ) 0             for             0 ϕ π ,
f ( ϕ ) = 0             for             π / K ϕ π ,
- π / K π / K d ϕ f ( ϕ ) = 1 .
a ^ + ( a ^ S IN + a ^ C IN ) / 2 ,
a ^ - ( a ^ S IN - a ^ C IN ) / 2 .
ψ IN = - d α + 1 - d α - 2 ψ 12 ( α + 1 , α - 2 ) α + 1 + 1 α - 2 - 2 ,
a ^ + 1 α + 1 + 1 = α + 1 α + 1 + 1 ,
a ^ - 2 α - 2 - 2 = α - 2 α - 2 - 2 .
ψ ˜ ( r , ϕ ) ψ 12 [ r cos ( ϕ ) , r sin ( ϕ ) ] ,
f ( ϕ ) 0 d r r ψ ˜ ( r , ϕ ) 2 .
a ^ S IN a ^ S IN + a ^ C IN a ^ C IN = a ^ + a ^ + + a ^ - a ^ - ,
N a ^ S IN a ^ S IN + a ^ C IN a ^ C IN = 0 d r r - π π d ϕ [ r 2 ψ ˜ ( r , ϕ ) 2 + 1 4 | ψ ˜ ( r , ϕ ) r | 2 + 1 4 r 2 | ψ ˜ ( r , ϕ ) ϕ | 2 - ψ ˜ ( r , ϕ ) 2 ] .
ψ r ( r ) exp ( - r / 2 σ ) r / 2 σ 3             for             0 r < ,
ψ ϕ ( ϕ ) { cos ( K ϕ / 2 ) K / π for 0 ϕ < π / K 0 for π / K ϕ π .
N = 12 σ 2 + ( K 2 + 1 ) / 32 σ 2 - 1.
N = 3 ( K 2 + 1 ) / 2 - 1 K 3 / 2             for             K 1.
f ( ϕ ) = { cos 2 ( K ϕ / 2 ) K / π for 0 ϕ < π / K 0 for π / K ϕ π .

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