Quantum non-signalling assisted zero-error classical capacity of qubit channels

TL;DR

This paper evaluates the one-shot quantum non-signalling assisted zero-error classical capacities of qubit channels, revealing that nonunital channels cannot transmit information with zero error under these conditions and that quantum non-signalling assistance is equivalent to entanglement assistance.

Contribution

It explicitly computes the capacities for qubit channels and shows the equivalence between quantum non-signalling and entanglement-assisted capacities in the one-shot setting.

Findings

Nonunital qubit channels have zero capacity with QNS assistance.

QNS assistance does not outperform entanglement assistance for qubit channels.

Capacities are explicitly evaluated for all qubit channels.

Abstract

In this paper, we explicitly evaluate the one-shot quantum non-signalling assisted zero-error classical capacities $\M_0^{\mathrm{QNS}}$ for qubit channels. In particular, we show that for nonunital qubit channels, $\M_0^{\mathrm{QNS}}=1$, which implies that in the one-shot setting, nonunital qubit channels cannot transmit any information with zero probability of error even when assisted by quantum non-signalling correlations. Furthermore, we show that for qubit channels, $\M_0^{\mathrm{QNS}}$ equals to the one-shot entanglement-assisted zero-error classical capacities. This means that for a single use of a qubit channel, quantum non-signalling correlations are not more powerful than shared entanglement.