Semiclassical model for a memory dephasing channel

TL;DR

This paper introduces a semiclassical model for a dephasing channel with memory, providing a way to describe correlations and their impact on quantum error correction performance.

Contribution

It proposes a Hamiltonian-based stochastic model for memory effects in dephasing channels and analyzes their influence on quantum coding.

Findings

Correlations among channel uses have minimal impact on three-qubit code performance.

Derived a general expression for coherence decay factors based on stochastic process spectrum.

Provided a framework to describe memory effects in quantum dephasing channels.

Abstract

We study a dephasing channel with memory, described by a Hamiltonian model in which the system-environment interaction is described by a stochastic process. We propose a useful way to describe the channel uses correlations. Moreover, we give a general expression for the coherences decay factors as a function of the number of channel uses and of the stochastic process power spectrum. We also study the impact of memory on the three qubit code, showing that correlations among channel uses affect very little the code performance.