The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any probability of error. In contrast to Shannon's standard channel capacity, which remains unaffected by preshared no-signaling correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of nonlocal correlations arising in the 2-2-$m$ Bell scenario, where two parties have two inputs and $m$ possible outcomes per input. For all $m\ge 2$, we construct examples of noisy classical channels with zero unassisted zero-error capacity that, when assisted by extremal 2-2-$m$ nonlocal correlations, can transmit one bit of information. Extending this analysis to the 2-$m$-2 Bell scenario, we identify channels with zero unassisted zero-error capacity that can nonetheless perfectly transmit $logm$ bits of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, we show that they can, however, enhance the success probability of one-shot transmission of classical messages. We also derive a nontrivial upper bound on the extent to which a given no-signaling correlation can activate the zero-error capacity of noisy classical channels. Finally, we show that the maximal zero-error communication advantage achievable with a no-signaling correlation lower bounds its classical simulation cost, thus linking its usefulness for communication to the classical cost of simulating it.

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• Quantum communication
• Quantum correlations, foundations & formalism
• Quantum foundations
• Quantum information processing