# Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

## TL;DR

This paper establishes an upper bound on the classical capacity of quantum channels with classical feedback, showing feedback does not enhance capacity for certain channels and introducing an information measure with key properties.

## Contribution

It introduces a novel entropy-based upper bound for quantum channel capacity with feedback and demonstrates its implications for specific channels like erasure and bosonic channels.

## Key findings

- Feedback does not increase capacity of quantum erasure channels.
- Energy constraints imply no capacity improvement for pure-loss bosonic channels.
- An information measure with specific properties underpins the entropy bound.

## Abstract

We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.