RELATION BETWEEN CHANNEL CAPACITY AND QUANTUM MINIMAX DECISION IN QUANTUM INFORMATION THEORY

摘要

In this paper, we have shown that the necessary condition of the information-optimum detection is satisfied by the optimum detection operators derived from the quantum minimax formula for the coherent state signals of binary, ternary and quadrature phase shift keyed. It is true that the condition is just only necessary condition, so that the information-optimum detection operators may be different from those by the quantum minimax formula. From the comparison by the numerical results, however, the mutual information obtained by these detection operators is much superior to those by conventional detectors and exists between Holevo's bound and the subentropy. Hence we make a conjecture that the mutual information attained by the optimum detection operators of the quantum minimax formula is the optimum mutual information for set of states with certain symmetry. In other words, the optimum detection operators by the quantum minimax formula describe the information-optimum detection processes for set of states with certain symmetry.rnFurthermore, the minimax condition is satisfied when all a priori probabilities of signals are equal each other for these signal quantum states. This situation corresponds to the maximization of the original information, namely, our obtained optimum mutual information will be the channel capacity for the code length one.