Bounding and Estimating the Classical Information Rate of Quantum Channels with Memory

TL;DR

This paper develops algorithms to estimate and bound the classical information rate of quantum channels with memory, using data-driven methods and graphical models, extending classical finite-state-channel techniques.

Contribution

It introduces novel algorithms for estimating and bounding the information rate of quantum channels with memory, leveraging auxiliary channels and data-driven learning.

Findings

Algorithms effectively estimate quantum channel information rates.

Auxiliary channels provide tight bounds on channel capacity.

Graphical models facilitate computations for quantum channels.

Abstract

We consider the scenario of classical communication over a finite-dimensional quantum channel with memory using a separable-state input ensemble and local output measurements. We propose algorithms for estimating the information rate of such communication setups, along with algorithms for bounding the information rate based on so-called auxiliary channels. Some of the algorithms are extensions of their counterparts for (classical) finite-state-machine channels. Notably, we discuss suitable graphical models for doing the relevant computations. Moreover, the auxiliary channels are learned in a data-driven approach; i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.

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