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arXiv:1508.01597 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise

Kentaro Kato

Published Sep 1, 2015• 2 citations
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Abstract

The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.

DOI
10.1117/12.2188103

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A new technique for evaluating the performance of quantum signals observed in the presence of 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-plusnoise 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 is characterized.
The necessary and sufficient conditions for the minimax strategy of a finite number of decisions in quantum signal detection are derived in the case that the average Bayes cost is used as a quality function. This is a simple extension of the result of Hirota and Ikehara [1]. Applying the necessary and sufficient conditions, a closed-form expression of the minimax strategy for binary pure state signal is shown. Furthermore, the minimax strategy for a discrimination problem of the quasi-Bell states is considered. In this case, the square-root measurement consisting of the quasi-Bell states yields the minimax strategy.