One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC

TL;DR

This paper introduces a new one-shot decoupling theorem for multi-sender quantum systems and develops a simultaneous decoding strategy for quantum multiple access channels, advancing quantum communication theory.

Contribution

It generalizes existing decoupling results to multiple senders and provides the first non-trivial simultaneous decoder for QMAC with limited entanglement.

Findings

Proves a novel one-shot multi-sender decoupling theorem.

Develops a one-shot simultaneous decoder for quantum multiple access channels.

Achieves a rate region analogous to the classical pentagonal region.

Abstract

In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard, Dein the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.