Parameter estimation by decoherence in the double-slit experiment

TL;DR

This paper investigates how quantum decoherence in a double-slit experiment can be used for parameter estimation of a scalar field's mass and coupling, revealing a link between fringe visibility and estimation precision.

Contribution

It introduces a non-perturbative analysis of decoherence effects on parameter estimation in a double-slit setup, connecting Fisher information with wave-particle duality.

Findings

Fringe pattern depends on scalar field mass and coupling.

Visibility relates to Fisher information for parameter estimation.

Fisher information characterizes wave-particle duality in the experiment.

Abstract

We discuss a parameter estimation problem using quantum decoherece in the double-slit interferometer. We consider a particle coupled to a massive scalar field after the particle passing through the double slit and solve the dynamics non-perturbatively for the coupling by the WKB approximation. This allows us to analyze the estimation problem which cannot be treated by master equation used in the research of quantum probe. In this model, the scalar field reduces the interference fringes of the particle and the fringe pattern depends on the field mass and coupling. To evaluate the contrast and the estimation precision obtained from the pattern, we introduce the interferometric visibility and the Fisher information matrix of the field mass and coupling. For the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the Fisher matrix. Also, focusing on the estimation precision of the mass, we find that the Fisher information characterizes the wave-particle duality in the double-slit interferometer.