Estimating the Information Rate of a Channel with Classical Input and Output and a Quantum State (Extended Version)

TL;DR

This paper introduces algorithms and graphical models for estimating the information rate of channels with classical inputs and outputs governed by evolving quantum states, extending classical methods to quantum-influenced channels.

Contribution

It proposes novel algorithms and graphical models to estimate the information rate of channels with quantum states, a significant extension of classical channel capacity estimation techniques.

Findings

Algorithms for estimating quantum-influenced channel capacity

Graphical models for quantum state evolution in channels

Bounding techniques for information rate with quantum states

Abstract

We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a \emph{classical} state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a \emph{quantum} state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.