Retrodiction for optical attenuators, amplifiers, and detectors

The transformation that an attenuator makes on the state of an optical field is the time reverse of that of an amplifier. Thus predicting the output state for an amplifier is equivalent to retrodicting the input state of an attenuator. We explore the consequences of this equivalence for simple optical quantum communication channels. One counterintuitive consequence is that the mean number of photons sent into an amplifier as retrodicted from a measurement of the number of output photons does not include the contribution of the amplifier noise.

[1]  D. D. Crouch,et al.  Quantum wideband traveling-wave analysis of a degenerate parametric amplifier , 1987 .

[2]  S M Barnett,et al.  Master equation for retrodiction of quantum communication signals. , 2001, Physical review letters.

[3]  S. Barnett,et al.  Retrodiction in quantum optics , 1999 .

[4]  Yoshihisa Yamamoto,et al.  Fundamentals of optical amplifiers , 1989 .

[5]  Paul D. Townsend.  Quantum Cryptography on Optical Fiber Networks , 1998 .

[6]  S. Stenholm.  The Theory of Quantum Amplifiers , 1986 .

[7]  Stephen M. Barnett,et al.  Imperfect photodetection as projection onto mixed states , 1998 .

[8]  Satosi Watanabe,et al.  Symmetry of Physical Laws. Part III. Prediction and Retrodiction , 1955 .

[9]  Stephen M. Barnett,et al.  Quantum retrodiction in open systems , 2002 .

[10]  S. Barnett,et al.  Optical state truncation , 1999 .

[11]  John von Neumann,et al.  Mathematical Foundations of Quantum Mechanics (Investigations in Physics No. 2) , 1955 .

[12]  Rodney Loudon,et al.  Theory of noise accumulation in linear optical-amplifier chains , 1985 .

[13]  Stephen M. Barnett,et al.  Bayes' theorem and quantum retrodiction , 2000, quant-ph/0106139.

[14]  R. Loudon,et al.  Optical Amplification and Spontaneous Emission in an Ar + Discharge , 1992 .

[15]  J. Lebowitz,et al.  TIME SYMMETRY IN THE QUANTUM PROCESS OF MEASUREMENT , 1964 .

[16]  Imoto,et al.  Quantum optics of traveling-wave attenuators and amplifiers. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[17]  Stephen M. Barnett,et al.  Retrodiction for quantum optical communications , 2000 .

[18]  R. Loudon,et al.  Properties of the Optical Quantum Amplifier , 1984 .