Periodicity in Ergodic Quantum Processes

TL;DR

This paper investigates the periodic behavior of quantum channel sequences from ergodic processes, linking these properties to spectral data and establishing a Perron-Frobenius-type theorem.

Contribution

It introduces a novel connection between periodicity in ergodic quantum processes and spectral analysis, providing a new theoretical framework.

Findings

Established a Perron-Frobenius-type theorem for quantum channels

Linked periodic properties to spectral data of quantum channels

Presented examples and open problems in the field

Abstract

We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the sequence of quantum channels, proving a general Perron-Frobenius-type theorem. We give examples to motivate the theory and conclude with some open problems and conjectures.