The private classical capacity and quantum capacity of a quantum channel
I. Devetak
TL;DR
The paper addresses private classical information capacity and quantum capacity of quantum channels, establishing a fundamental link between privacy and coherence. It shows that the private classical capacity $C_p$ and secret-key capacity $K$ for both classical-quantum wiretap channels and quantum channels coincide with coherent-information-based expressions, notably $C_p({\cal N})=K({\cal N})= \lim_{l\to\infty} (1/l) \max_{\rho} I_p(\rho,{\cal N}^{\otimes l})$ and, for entanglement generation and quantum transmission, that the entanglement-generation capacity $E({\cal N})$ and quantum capacity $Q({\cal N})$ both equal the regularized coherent-information rate $\lim_{l\to\infty} (1/l) \max_{\rho} I_c(\rho,{\cal N}^{\otimes l})$. By coherently converting secret-key protocols into entanglement-generation protocols, the authors derive a new, simpler proof of the quantum capacity theorem and show that forward public communication does not enhance these capacities. The work unifies quantum privacy and coherence under a common information-theoretic framework and clarifies the operational roles of coherent information in multiple channel capacities.
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.