Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels

TL;DR

This paper introduces the classes of more capable and less noisy quantum channels, analyzing their capacities and showing conditions under which private and quantum capacities coincide or can be characterized simply.

Contribution

It defines new classes of quantum channels and establishes their capacity properties, including conditions for capacity equivalence and single-letter characterizations.

Findings

Quantum capacities of complementary channels are zero for more capable channels.

Private and quantum capacities coincide for more capable channels.

Capacities of less noisy channels can be characterized with single-letter formulas.

Abstract

Two new classes of quantum channels, which we call more capable and less noisy, are introduced. The more capable class consists of channels such that the quantum capacities of the complementary channels to the environments are zero. The less noisy class consists of channels such that the private capacities of the complementary channels to the environment are zero. For the more capable class, it is clarified that the private capacity and quantum capacity coincide. For the less noisy class, it is clarified that the private capacity and quantum capacity can be single letter characterized.