Localization by Dissipative Disorder: a Deterministic Approach to Position Measurements

TL;DR

This paper introduces a deterministic method for position measurement in quantum systems using dissipative disordered potentials that induce localization and replicate the Born rule.

Contribution

It presents a novel approach linking dissipative disordered potentials to quantum localization, offering a deterministic framework for position measurements.

Findings

Dissipative disordered potentials cause Anderson localization of wavefunctions.

The approach reproduces the Born probability rule.

Numerical simulations confirm the consistency of the method.

Abstract

We propose an approach to position measurements based on the hypothesis that the action of a position detector on a quantum system can be effectively described by a dissipative disordered potential. We show that such kind of potential is able, via the dissipation-induced Anderson localization, to contemporary localize the wavefunction of the system and to dissipate information to modes bounded to the detector. By imposing a diabaticity condition we demonstrate that the dissipative dynamics between the modes of the system leads to a localized energy exchange between the detector and the rest of the environment -the "click" of the detector- thus providing a complete deterministic description of a position measurement. We finally numerically demonstrate that our approach is consistent with the Born probability rule.