Centralised multi link measurement compression with side information

TL;DR

This paper introduces nearly optimal one shot measurement compression bounds for quantum instruments with side information, advancing quantum information theory by removing the need for catalytic randomness and generalizing to multi link scenarios.

Contribution

It presents the first nearly optimal one shot bounds for centralised multi link measurement compression with quantum side information, without requiring catalytic randomness.

Findings

Nearly optimal one shot bounds established

Introduces a novel sequential classical-quantum covering lemma

Results recover standard asymptotic iid measurement compression

Abstract

We prove new one shot achievability results for measurement compression of quantum instruments with side information at the receiver. Unlike previous one shot results for this problem, our one shot bounds are nearly optimal and do not need catalytic randomness. In fact, we state a more general problem called centralised multi link measurement compression with quantum side information and provide one shot achievability results for it. As a simple corollary, we obtain one shot measurement compression results for quantum instruments with side information that we mentioned earlier. All our one shot results lead to the standard results for this problem in the asymptotic iid setting. We prove our achievability bounds by first proving a novel sequential classical quantum multipartite covering lemma, which should be of independent interest.