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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum detection of signals in the presence of noise

Victor A. Vilnrotter, Chi-Wung Lau

Published Jul 7, 2003• 5 citations
Publisher

Abstract

A new technique for evaluating the performance of quantum signals observed in the presence noise is described and evaluated. The quantum theory for detecting coherent-state signals has been developed previously, however the quantum "signal plus noise" problem has received little attention due to its complexity. Here we develop a discrete approximation to the coherent-state representation of signal-plus-noise density operators, and present solutions to optimum receiver performance in terms of quantum "measurement states" whose performance is optimized via generalized rotations in Hilbert space. An efficient algorithm for carrying out the required numerical optimization is described and applied to binary signals observed in the presence of noise, for which exact results are available for comparison. The algorithm is then applied to the detection of ternary signals observed in the presence of noise, a previously unsolved problem, and the performance of the optimum receiver characterized.

DOI
10.1117/12.478929

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The fundamental performance limits and channel capacity of optical commu-nications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse-position modulation, which requires a product state representation, will be evaluated along with the performance of certain dense signal sets. Perfor-mance comparisons with classical techniques show an improvement of over 5 dB in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting. I.
Methods are presented for calculating the minimum attainable probability of error in detecting a coherent quantum signal received amid thermal noise in the limits of low and high signal-to-noise ratio. In the latter limit, quantum-mechanical perturbation theory is applied to solving the detection operator equation approximately. Graphic results are furnished for binary signals transmitted with equal prior probabilities. Previous work on this problem is thus extended to a broader range of signal and noise strengths. The results are applied to the detection of antipodal two-photon-coherent-state signals. (Author)
The fundamental performance limits and channel capacity of optical communications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse-position modulation, which requires a product state representation, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.
This paper is concerned with the minimax strategy in quantum signal detection theory. First we show a numerical calculation method for finding a solution to the quantum minimax decision problem in the case that the average probability of decision errors is used as the quality function of a quantum communication system. To verify the numerical calculation method, ternary coherent state signal is considered in the absence of thermal noise. After that, the error probability of the quantum minimax receiver for the ternary coherent state signal in the pressure of thermal noise is computed by using this numerical calculation method.