On entanglement assistance to a noiseless classical channel

TL;DR

This paper demonstrates that entanglement assistance can enhance the success probability of classical communication over a noiseless channel, and that a single extra classical bit can replace the quantum entanglement resource.

Contribution

It proves that bipartite quantum entanglement can be simulated by just one additional classical bit in noiseless communication tasks.

Findings

Entanglement can improve success probabilities in one-shot noiseless channels.

A single classical bit suffices to replicate the advantage of entanglement.

No upper bound exists for classical resources replacing general non-signaling assistance.

Abstract

For a classical channel, neither the Shannon capacity, nor the sum of conditional probabilities corresponding to the cases of successful transmission can be increased by the use of shared entanglement, or, more generally, a non-signaling resource. Yet, perhaps somewhat counterintuitively, entanglement assistance can help and actually elevate the chances of success even in a one-way communicational task that is to be completed by a single-shot use of a noiseless classical channel. To quantify the help that a non-signaling resource provides to a noiseless classical channel, one might ask how many extra letters should be added to the alphabet of the channel in order to perform equally well without the specified non-signaling resource. As was observed by Cubitt, Leung, Matthews, and Winter, there is no upper bound on the number of extra letters required for substituting the assistance of a general non-signaling resource to a noiseless one-bit classical channel. In contrast, here we prove that if this resource is a bipartite quantum system in a maximally entangled state, then an extra classical bit always suffices as a replacement.