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Error Performance of Quantum Minimax Receiver for 16QAM Coherent State Signal

Kentaro Kato

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Recently a numerical calculation method for nding the minimax solution to the minimax problem in quantum signal detection was reported [10]. In this paper, we evaluate the error performance of the minimax receiver for 16QAM coherent state signal by using this calculation method. Through this numerical simulation, it will be pointed out that the use of the minimax strategy has an advantage rather than that of the Bayes strategy in designing quantum communication systems.

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Recently a numerical calculation method for nding the minimax solution to the minimax problem in quantum signal detection was reported [10]. In this paper, we evaluate the error performance of the minimax receiver for 16QAM coherent state signal by using this calculation method. Through this numerical simulation, it will be pointed out that the use of the minimax strategy has an advantage rather than that of the Bayes strategy in designing quantum communication systems.
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.
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.
We consider the application of the minimax strategy to discrimination between quantum states with a certain fraction of inconclusive results. An inconclusive minimax solution is defined as the pair of a collection of prior probabilities and a quantum measurement that achieves the minimax probability of a detection error subject to the constraint that the highest probability of an inconclusive result does not exceed a given value. We first show a necessary and sufficient condition for an inconclusive minimax solution, and derive that the problem of obtaining an inconclusive minimax measurement can be expressed as a semidefinite programming problem. We then present a condition under which there exists a solution such that at least one of the prior probabilities is a zero. We finally show that for any state set with a certain symmetry, an inconclusive minimax solution exists having the same symmetry.