Trading classical communication, quantum communication, and entanglement in quantum Shannon theory

TL;DR

This paper establishes trade-offs and capacity theorems for classical, quantum communication, and entanglement in quantum Shannon theory, introducing new protocols and matching converses for static and dynamic scenarios.

Contribution

It provides the first comprehensive capacity theorems with matching converses for the interplay of classical, quantum, and entanglement resources in both static and dynamic settings.

Findings

Derived a unit-resource capacity theorem for noiseless resources.

Proposed the classically-assisted state redistribution protocol.

Established achievable rate regions with matching multi-letter converses.

Abstract

We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, super-dense coding, and entanglement distribution. We then provide an achievable rate region and a matching multi-letter converse for the direct static capacity theorem. This theorem applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). Our coding strategy involves a protocol that we name the classically-assisted state redistribution protocol and the three fundamental protocols. We finally provide an achievable rate region and a matching mutli-letter converse for the direct dynamic capacity theorem. This theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources. Our coding strategy combines the classically-enhanced father protocol with the three fundamental unit protocols.