Fermionic Markov Chains

TL;DR

This paper introduces a quantum analogue of classical Markov processes using free Fermions, calculates their entropy density, and extends Szeg"o's theorem to rate functions for asymptotic analysis.

Contribution

It constructs free Fermionic Markov processes and extends Szeg"o's theorem to compute entropy densities in this quantum setting.

Findings

Entropy density for free Fermionic processes calculated

Extension of Szeg"o's theorem to rate functions presented

Provides a method for analyzing quantum Markov processes

Abstract

We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.