Theoretical Analysis of Parameter Estimation by Quantum Decoherence for the Double-slit Thought Experiment
Akira Matsumura, Taishi Ikeda, Shingo Kukita
When individual particles pass through a double slit, a fringe pattern appears on a screen. If an observer detects the path of the particle, the interference fringes disappear. This is called the quantum decoherence. In this paper, we discuss a parameter estimation problem using the quantum decohenrece in the double-slit experiment. As a simple model, we consider a massive scalar field interacting with the particle which have passed through the double slit. The scalar field, as well as the observer, can induce the loss of the fringe pattern of the particle. Because the interference fringes of the particle depend on the field mass and coupling, we can estimate the field parameters from the fringes. For qualitative analysis, we introduce the interferometric visibility of the fringe pattern and the Fisher information (FI) matrix of the field mass and coupling. Using the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the FI matrix. Also if we focus on FI of the mass, then we find that FI characterizes the wave-particle duality in the double-slit experiment.
•Oct 18, 2017•0 citations