On the near-optimality of one-shot classical communication over quantum channels

TL;DR

This paper demonstrates near-optimal classical communication over various quantum channels in one-shot scenarios, using position-based decoding, without relying on simultaneous decoding strategies.

Contribution

It introduces a unified approach to characterize communication limits in multiple quantum network scenarios using position-based decoding.

Findings

Achieves near-optimal communication bounds in one-shot quantum channels.

Provides a simple proof of the converse for entanglement-assisted quantum channel coding.

Extends the approach to complex network scenarios without requiring simultaneous decoding.

Abstract

We study the problem of transmission of classical messages through a quantum channel in several network scenarios in the one-shot setting. We consider both the entanglement assisted and unassisted cases for the point to point quantum channel, quantum multiple-access channel, quantum channel with state and the quantum broadcast channel. We show that it is possible to near-optimally characterize the amount of communication that can be transmitted in these scenarios, using the position-based decoding strategy introduced in a prior work [Anshu, Jain and Warsi, 2017]. In the process, we provide a short and elementary proof of the converse for entanglement-assisted quantum channel coding in terms of the quantum hypothesis testing divergence (obtained earlier in [Matthews and Wehner, 2014]). Our proof has the additional utility that it naturally extends to various network scenarios mentioned above. Furthermore, none of our achievability results require a simultaneous decoding strategy, existence of which is an important open question in quantum Shannon theory.