# 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.

## Key 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.