An Additive Refinement of Quantum Channel Capacities

Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity measure. 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 using restricted encodings, we prove additive quantities for quantum channel capacities that can be employed for quantum Shannon theorems. This refinement is consistent with the principles of quantum theory, and it further demonstrates von Neumann entropy as the cornerstone of quantum information.