On Feedback and the Classical Capacity of a Noisy Quantum Channel

TL;DR

This paper demonstrates that classical feedback does not enhance the classical capacity of certain noisy quantum channels, extending Shannon's classical results to specific quantum communication scenarios.

Contribution

It generalizes Shannon's classical feedback capacity results to quantum channels, showing no capacity increase with feedback for non-entangled inputs and entanglement-breaking channels.

Findings

Feedback does not increase capacity for non-entangled input states.

Feedback does not increase capacity for entanglement-breaking channels.

Extends classical feedback capacity results to quantum communication.

Abstract

In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this paper the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across non-entangled input states, or when the channel is an entanglement--breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.