Classical capacity of quantum channels with general Markovian correlated noise

TL;DR

This paper derives the classical capacity of quantum channels affected by general Markovian correlated noise, including channels with long-term memory, by relating capacity to the properties of the underlying Markov chain.

Contribution

It provides a new capacity formula for quantum channels with arbitrary Markovian correlated noise, extending previous results to channels with long-term memory.

Findings

Capacity expressed via communicating classes of the Markov chain

Capacity formula reduces to known results for forgetful channels

Addresses channels with non-converging Markov chains

Abstract

The classical capacity of a quantum channel with arbitrary Markovian correlated noise is evaluated. For the general case of a channel with long-term memory, which corresponds to a Markov chain which does not converge to equilibrium, the capacity is expressed in terms of the communicating classes of the Markov chain. For an irreducible and aperiodic Markov chain, the channel is forgetful, and one retrieves the known expression for the capacity.