Nonlocality-Assisted Enhancement of Error-Free Communication in Noisy Classical Channels

TL;DR

This paper demonstrates how nonlocal correlations, especially from Bell scenarios, can enhance zero-error communication in noisy classical channels, enabling error-free transmission of information that is otherwise impossible.

Contribution

It introduces new examples of noisy channels that achieve positive zero-error capacity with nonlocal correlations, highlighting their utility beyond quantum entanglement.

Findings

Nonlocal correlations can enable error-free transmission in channels with zero zero-error capacity.

Quantum entangled states cannot achieve positive zero-error capacity in these scenarios.

Bell nonlocal correlations can transmit log m bits perfectly in certain channels.

Abstract

The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.