# Dense coding capacity of a quantum channel

## TL;DR

This paper determines the maximum rate of classical information transfer using dense coding over noisy quantum channels, specifically Pauli channels, by optimizing adaptive strategies and employing advanced quantum information techniques.

## Contribution

It introduces a method to compute the dense coding capacity of Pauli channels in any finite dimension, providing explicit formulas for common noise models like depolarizing and dephasing channels.

## Key findings

- Derived the dense coding capacity formulas for Pauli channels.
- Established capacity bounds for depolarizing and dephasing qubit channels.
- Utilized channel simulation and protocol stretching techniques.

## Abstract

We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum channel, we define its dense coding capacity by optimizing over all adaptive strategies that Alice can implement, while Bob encodes the information by means of Pauli operators. Exploiting techniques of channel simulation and protocol stretching, we are able to establish the dense coding capacity of Pauli channels in arbitrary finite dimension, with simple formulas for depolarizing and dephasing qubit channels.