On approximation of infinite-dimensional quantum channels
Максим Евгеньевич Широков, Alexander Semenovich Holevo · Problems of Information Transmission · 2008
We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ -capacity as a function of a channel, strong additivity of the χ -capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.