Entanglement-assisted communication of classical and quantum information

TL;DR

This paper establishes a capacity theorem for transmitting classical and quantum information over entanglement-assisted quantum channels, introducing a new protocol that outperforms time-sharing strategies in certain cases.

Contribution

It introduces the classically-enhanced father protocol, a general quantum communication protocol that improves capacity bounds and unifies previous protocols.

Findings

Capacity region characterized by a three-dimensional rate triple

Classically-enhanced father protocol generalizes existing quantum protocols

Improves over time-sharing strategy for qubit dephasing channel

Abstract

We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the region are rate triples, consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The crucial protocol in achieving the boundary points of the capacity region is a protocol that we name the classically-enhanced father protocol. The classically-enhanced father protocol is more general than other protocols in the family tree of quantum Shannon theoretic protocols, in the sense that several previously known quantum protocols are now child protocols of it. The classically-enhanced father protocol also shows an improvement over a time-sharing strategy for the case of a qubit dephasing channel--this result justifies the need for simultaneous coding of classical and quantum information over an entanglement-assisted quantum channel. Our capacity theorem is of a multi-letter nature (requiring a limit over many uses of the channel), but it reduces to a single-letter characterization for at least three channels: the completely depolarizing channel, the quantum erasure channel, and the qubit dephasing channel.