Public Quantum Communication and Superactivation

TL;DR

This paper explores the concept of public quantum communication through symmetric-side channels, revealing their role in entanglement distillation, quantum privacy, and superactivation of quantum channel capacity, thus providing new insights into quantum information theory.

Contribution

It introduces symmetric-side channels as a quantum analogue of public communication, demonstrating their impact on entanglement and capacity superactivation, and linking privacy amplification to non-additivity of quantum capacity.

Findings

Symmetric-side channels equalize distillable entanglement and mutual independence.

Assistance by symmetric-side channels enables superactivation of quantum capacity.

Single-copy superactivation can be viewed as converting mutual independence into entanglement.

Abstract

Is there a meaningful quantum counterpart to public communication? We argue that the symmetric-side channel -- which distributes quantum information symmetrically between the receiver and the environment -- is a good candidate for a notion of public quantum communication in entanglement distillation and quantum error correction. This connection is partially motivated by [Brand\~ao and Oppenheim, arXiv:1004.3328], where it was found that if a sender would like to communicate a secret message to a receiver through an insecure quantum channel using a shared quantum state as a key, then the insecure quantum channel is only ever used to simulate a symmetric-side channel, and can always be replaced by it without altering the optimal rate. Here we further show, in complete analogy to the role of public classical communication, that assistance by a symmetric-side channel makes equal the distillable entanglement, the recently-introduced mutual independence, and a generalization of the latter, which quantifies the extent to which one of the parties can perform quantum privacy amplification. Symmetric-side channels, and the closely related erasure channel, have been recently harnessed to provide examples of superactivation of the quantum channel capacity. Our findings give new insight into this non-additivity of the channel capacity and its relation to quantum privacy. In particular, we show that single-copy superactivation protocols with the erasure channel, which encompasses all examples of non-additivity of the quantum capacity found to date, can be understood as a conversion of mutual independence into distillable entanglement.