Quantum walk, entanglement and thermodynamic laws

TL;DR

This paper explores the thermodynamic properties of a quantum walk on a line, analyzing entropy and energy changes between stationary states induced by measurements, and applying thermodynamic laws to this quantum process.

Contribution

It introduces a thermodynamic framework for quantum walks involving entanglement, measurements, and stationary states, linking quantum dynamics to thermodynamic laws.

Findings

Entropy change bounds depend on initial conditions

Energy change corresponds to heat transfer

Thermodynamic laws apply to quantum walk dynamics

Abstract

We consider an special dynamics of a quantum walk (QW) on a line. Initially, the walker localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is performed and the state resulting from this measurement is used to start a second QW evolution to achieve a second asymptotic stationary state. In previous works, we developed the thermodynamics associated with the entanglement between the coin and position degrees of freedom in the QW. Here we study the application of the first and second laws of thermodynamics to the process between the two stationary states mentioned above. We show that: i) the entropy change has upper and lower bounds that are obtained analytically as a function of the initial conditions. ii) the energy change is associated to a heat-transfer process.