Necessary and sufficient conditions for minimax strategy in quantum signal detection

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.