One-Shot Triple-Resource Trade-Off in Quantum Channel Coding

TL;DR

This paper investigates the simultaneous classical and quantum communication over noisy quantum channels with limited shared entanglement, providing bounds on the one-shot capacity region using smooth conditional entropies.

Contribution

It introduces new direct and converse bounds for the one-shot capacity region of quantum channels, utilizing the generalized randomized partial decoupling theorem.

Findings

Bounds match in the asymptotic limit for memoryless channels

Results generalize previous work by Hsieh and Wilde

Applicable to various communication tasks in quantum information

Abstract

We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity region, represented by the smooth conditional entropies and the error tolerance. The proof is based on the randomized partial decoupling theorem, which is a generalization of the decoupling theorem. The two bounds match in the asymptotic limit of infinitely many uses of a memoryless channel and coincide with the previous result obtained by Hsieh and Wilde. Direct and converse bounds for various communication tasks are obtained as corollaries, both for the one-shot and asymptotic scenarios.