Parameter estimation by decoherence in the double-slit 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.

25 pages, 8 figures

References in corpus (6)

• Decoherence of matter waves by thermal emission of radiation
• Qubit metrology and decoherence
• Continuous-variable quantum probes for structured environments
• Quantum Fisher Information as a Predictor of Decoherence in the Preparation of Spin-Cat States for Quantum Metrology
• Can quantum probes satisfy the weak equivalence principle?
• N-body-extended Channel Estimation for Low-Noise Parameters