# Computing Quantum Channel Capacities

## TL;DR

This paper extends classical Blahut-Arimoto algorithms to quantum channels, providing efficient iterative methods to compute various quantum capacities with proven error bounds and demonstrating fast convergence through numerical experiments.

## Contribution

It introduces quantum generalizations of classical capacity algorithms, enabling accurate and efficient computation of multiple quantum channel capacities.

## Key findings

- Algorithms converge rapidly in numerical tests.
- Rigorous bounds on estimation errors are established.
- Methods applicable to classical-quantum and quantum channels.

## Abstract

The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating optimization schemes, called Blahut-Arimoto algorithms. In this work, we generalize classical Blahut-Arimoto algorithms to the quantum setting. In particular, we give efficient iterative schemes to compute the capacity of channels with classical input and quantum output, the quantum capacity of less noisy channels, the thermodynamic capacity of quantum channels, as well as the entanglement-assisted capacity of quantum channels. We give rigorous a priori and a posteriori bounds on the estimation error by employing quantum entropy inequalities and demonstrate fast convergence of our algorithms in numerical experiments.