An additive refinement of quantum channel capacities

TL;DR

This paper introduces a refined approach to quantum channel capacities that achieves additivity, simplifying the analysis of quantum information transmission and emphasizing the central role of von Neumann entropy.

Contribution

It proposes a minimal refinement of quantum communication settings to obtain additive capacities, facilitating quantum Shannon theorems and advancing understanding of quantum information.

Findings

Established additive quantum channel capacities under the refined setting

Demonstrated the consistency of the refinement with quantum theory principles

Highlighted von Neumann entropy as fundamental in quantum information

Abstract

Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as capacity measures. Asymptotic regularization is generically necessary making the study of capacities notoriously hard. In this work, by a proper refinement of the physical settings of quantum communication, we prove additive quantities for quantum channel capacities that can be employed for quantum Shannon theorems. This refinement, only a tiny step away from the standard settings, is consistent with the principle of quantum theory, and it further demonstrates von Neumann entropy as the cornerstone of quantum information.