# Applications of position-based coding to classical communication over quantum channels

## TL;DR

This paper explores the use of position-based coding in quantum communication, establishing bounds and rate regions for classical communication over quantum channels, and linking decoding conjectures to quantum hypothesis testing.

## Contribution

It applies position-based coding to entanglement-assisted quantum communication, deriving new bounds and reducing complex decoding conjectures to hypothesis testing problems.

## Key findings

- Lower bounds for error exponents and second-order coding rates.
- Achievable rate regions for quantum multiple access channels.
- Reduction of quantum decoding conjecture to hypothesis testing questions.

## Abstract

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Renyi-2 entropies and conditional quantum entropies.