Many body physics and the capacity of quantum channels with memory

TL;DR

This paper explores how correlations in quantum channel errors, modeled via many-body physics, affect channel capacity, providing a rigorous foundation for analyzing such systems and revealing complex behaviors.

Contribution

It establishes key technical properties for many-body systems used to model correlated quantum errors, enabling rigorous analysis of channel capacities with memory.

Findings

Connected quantum channel capacity with many-body physics.

Established technical properties for classes of many-body systems.

Facilitated understanding of non-analytic behaviors in correlated errors.

Abstract

In most studies of the capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this article we discuss these properties in detail, and establish them for some classes of many-body system.