Transient temperature and mixing times of quantum walks on cycles

TL;DR

This paper extends the concept of entanglement temperature to quantum walks on cycles, revealing a linear relationship between thermalization and mixing times, which become size-insensitive for larger systems.

Contribution

It introduces a new framework for entanglement temperature in quantum walks on cycles and uncovers their thermalization and mixing time behaviors.

Findings

Linear connection between thermalization and mixing times.

Characteristic times become insensitive to system size for large N.

Extension of entanglement temperature concept to N-cycles.

Abstract

The definition of entanglement temperature for the quantum walk on the line is extended to $N$-cycles, which are more amenable to a physical implementation. We show that, for these systems, there is a linear connection between the thermalization time and the mixing time, and also that these characteristic times become insensitive to the system size when $N$ is larger than a few units