On optimal entanglement assisted one-shot classical communication

TL;DR

This paper characterizes the optimal entanglement-assisted strategies for one-shot classical communication over noisy channels, providing a complete framework to construct and analyze such protocols, including bounds on quantum and no-signaling enhancements.

Contribution

It offers a full characterization of optimal entanglement-assisted protocols via operator set radii, enabling protocol construction and limit proofs for classical channels.

Findings

Prevedel et al. protocol is optimal for two-qubit entanglement.

Established bounds on quantum and no-signaling correlation improvements.

Provided a method to construct optimal protocols from classical channel data.

Abstract

The one-shot success probability of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be sent via a single use of the channel. Prevedel et al. (PRL 106, 110505 (2011)) recently showed that for a specific channel, this quantity can be increased if the parties using the channel share an entangled quantum state. We completely characterize the optimal entanglement-assisted protocols in terms of the radius of a set of operators associated with the channel. This characterization can be used to construct optimal entanglement-assisted protocols from the given classical channel and to prove the limit of such protocols. As an example, we show that the Prevedel et al. protocol is optimal for two-qubit entanglement. We also prove some simple upper bounds on the improvement that can be obtained from quantum and no-signaling correlations.