AN OPERATIONAL ALGEBRAIC APPROACH TO QUANTUM CHANNEL CAPACITY

Abstract

An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of informational divergences, namely, Araki–Umegaki (a-type) and of Belavkin–Staszewski (b-type) quantum relative entropic information, this paper treats two types of quantum mutual information via entanglement and defines two types of corresponding quantum channel capacities as the supremum via the generalized encodings. It proves the additivity property of quantum channel capacities via entanglement, which extends the earlier results of Belavkin to products of arbitrary quantum channels for quantum relative entropy of any type.