Superadditivity of Zero-Error Capacity in Noisy Classical and Perfect Quantum Channel Pairs

TL;DR

This paper shows that combining a noisy classical channel with a perfect quantum channel can enable transmitting more messages than the sum of their individual capacities, highlighting a quantum advantage rooted in contextuality.

Contribution

It provides explicit constructions demonstrating superadditivity of zero-error capacity in classical-quantum channel pairs and identifies the structural and contextuality conditions for this effect.

Findings

Superadditivity of zero-error capacity demonstrated

Quantum advantage linked to Kochen-Specker contextuality

Replacing quantum with classical channel removes superadditivity

Abstract

We demonstrate superadditivity of one-shot zero-error classical capacity in an asymmetric communication setting where a noisy classical channel is used in parallel with a perfect quantum channel. Each channel individually supports only a fixed number of perfectly distinguishable messages. Their joint use enables transmission of strictly more messages than permitted by the product of the individual capacities. We present explicit constructions achieving this enhancement and establish that replacing the perfect quantum channel with a perfect classical channel eliminates the effect. Finally, we identify a structural criterion on the noisy channel governing this effect and show that the quantum advantage is rooted in Kochen-Specker contextuality.