The quantum walk temperature

TL;DR

This paper develops a thermodynamic framework to analyze entanglement dynamics in quantum walks, revealing that a steady state can emerge despite the underlying unitary evolution, which has implications for understanding quantum thermodynamics.

Contribution

It introduces a thermodynamic theory for quantum walk entanglement, showing steady states can form in unitary systems through Markovian transient stages.

Findings

A steady state emerges in quantum walks despite unitary evolution.

Entanglement behavior can mask the unitary nature of the global system.

The theory applies to composite Hilbert spaces with tensor product structures.

Abstract

A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. This theory shows that, in spite of the unitary evolution, a steady state is established after a Markovian transient stage. This study suggests that if a quantum dynamics is developed in a composite Hilbert space (i.e. the tensor product of several sub-spaces) then the behavior of an operator that only belongs to one of the sub-spaces may camouflage the unitary character of the global evolution.