The Private Classical Capacity and Quantum Capacity of a Quantum Channel

TLDR

Motivated by Schumacher and Westmoreland, the coherent information underlies capacities for private classical information, secret key generation, and pure bipartite entanglement. The authors aim to derive a formula for the capacity of a quantum channel to transmit private classical information and to generate pure bipartite entanglement. By exploiting parallels between private classical information and quantum information, the authors derive an expression for the channel capacity. The capacity equals the secret key capacity, is not increased by forward public classical communication, and its derivation provides a new proof of the quantum channel coding theorem and a simple converse.

Abstract

A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities