Improving zero-error classical communication with entanglement

TL;DR

This paper demonstrates that entanglement can enhance zero-error classical communication over certain channels, introducing new constructions based on Bell-Kochen-Specker proofs and exploring connections to pseudo-telepathy and non-signalling correlations.

Contribution

It introduces a method to increase zero-error message capacity using entanglement and constructs channels from Bell-Kochen-Specker proofs, advancing quantum classical communication theory.

Findings

Entanglement increases zero-error message capacity for certain channels.

Channels based on Bell-Kochen-Specker proofs enable zero-error communication with entanglement.

Non-signalling correlations can sometimes enable zero-error communication without unassisted capacity.

Abstract

Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behaviour constitutes the field of classical zero-error information theory, the quantum generalisation of which has started to develop recently. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent with no chance of error. In particular, we show how to construct such a channel based on any proof of the Bell-Kochen-Specker theorem. This is a new example of the use of quantum effects to improve the performance of a classical task. We investigate the connection between this phenomenon and that of ``pseudo-telepathy'' games. The use of generalised non-signalling correlations to assist in this task is also considered. In this case, a particularly elegant theory results and, remarkably, it is sometimes possible to transmit information with zero-error using a channel with no unassisted zero-error capacity.