On Quantum Semipermeable Barriers: Investigating Maxwell's Demon Toolbox

TL;DR

This paper models a quantum Maxwell's demon with a semipermeable barrier in a discrete space-time system, revealing how quantum properties and auxiliary systems influence particle dynamics and barrier functionality.

Contribution

It introduces a local unitary dynamics framework for quantum semipermeable barriers, incorporating an auxiliary system to analyze quantum effects on particle confinement and barrier behavior.

Findings

Particles cannot be trapped indefinitely unless the auxiliary system is infinite.

Quantum coherence and correlations are altered by the barrier.

Superpositions of the auxiliary system enable the barrier to function as a beam splitter.

Abstract

We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilises an auxiliary system $\mathcal{A}$ and we study how properties of $\mathcal{A}$ influence the behaviour of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless $\mathcal{A}$ is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of $\mathcal{A}$ allows the barrier to act as a beam splitter.