Measurements on an Anderson Chain

TL;DR

This paper investigates how local measurements affect the dynamics of a quantum particle in an Anderson-localized system, revealing measurement-induced delocalization and controllable transport.

Contribution

It demonstrates how random and controlled measurements influence localization and transport in an Anderson chain, providing insights into measurement effects on quantum localization.

Findings

Random measurements delocalize the average position.

Quantum trajectories remain localized with a modified length.

Controlled measurements enable targeted localization and transport.

Abstract

We study the dynamics of a monitored single particle in a one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local, projective measurements. The competition between disorder-induced localization and measurement-induced jumps leads to interesting behaviour of readout-averaged quantities. We find that measurements at random positions delocalize the average position, similar to a classical random walk. Along each quantum trajectory, the particle remains localized, however with a modified localization length. In contrast to measurement-induced delocalization, controlled measurements can be used to introduce transport in the system and localize the particle at a chosen site. In this sense, the measurements provide a controlled environment for the particle.