Classical capacity of a qubit depolarizing memory channel with Markovian correlated noise

TL;DR

This paper investigates the classical capacity of a quantum memory channel with Markovian correlated noise, revealing how entanglement and channel parameters influence capacity, and conjecturing capacity behavior for larger input sizes.

Contribution

It introduces a model of a forgetful quantum memory channel with Markovian switching and analyzes how different input states affect classical capacity.

Findings

Maximally entangled states or product states optimize capacity depending on parameters.

Numerical evidence suggests capacity approaches product state capacity as input size increases.

Capacity depends on depolarizing channel parameters and Markov chain memory.

Abstract

We study the classical capacity of a forgetful quantum memory channel that switches between two qubit depolarizing channels according to an ergodic Markov chain. The capacity of this quantum memory channel depends on the parameters of the two depolarizing channels and the memory of the ergodic Markov chain. When the number of input qubit's is two, we show that depending on channel parameters either the maximally entangled input states or product input states achieve the classical capacity. Our conjecture based on numerics is that as the number of input qubits are increased the classical capacity approaches the product state capacity for all values of the parameters.