Relation between Channel Capacity and Quantum Minimax Decision in Quantum Information Theory

Abstract

Derivation of the optimum detection operators for the mutual information is one of the most important topics to establish the quantum information theory. For information-optimum detection, Holevo has shown a necessary condition of the information-optimum detection operators [1]. However, the explicit representation of the information-optimum detection operators has not been given except for a few cases [24]. So far there were researches about the upper or lower bound of the accessible information which is the optimum (maximum) mutual information for given signal quantum states with coding theory. In the general case, the upper bound is given by Holevo, called “Holevo’s bound” [5] and the lower bound is the “subentropy” defined by Jozsa [6]. In some cases of specified signal quantum states and detection process, Ban and Schumacher showed tighter upper bounds, respectively [7, 8].