One-shot inner bounds for sending private classical information over a quantum MAC

TL;DR

This paper establishes the first inner bounds for private classical communication over quantum multiple access channels using advanced information theoretic techniques, including a novel smoothed distributed covering lemma.

Contribution

It introduces a new smoothed distributed covering lemma and applies recent techniques to derive one-shot inner bounds for quantum MACs, advancing quantum information theory.

Findings

First inner bounds for private classical info over quantum MACs

Introduction of a new smoothed distributed covering lemma

Bounds match classical analogues in the asymptotic iid setting

Abstract

We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem.