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Event by event method for quantum interference simulation

M Delina

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Event by event method is a simulation approach which is not based on the knowledge of the Schrodinger equation. This approach uses the classical wave theory and particle concept: we use particles, not waves. The data is obtained by counting the events that were detected by the detector, just as in real experiments. The particle is considered as a messenger (carries a message) that is processed by the deterministic learning machine. We demonstrated that the event-based deterministic learning machine simulation can produce the same interference patterns as those obtained in the experiment. The event-by-event method reproduces the results of quantum theory of the Mach-Zehnder interferometer, Mach-Zehnder interferometer with absorber, three beam interference, delayed choice and two-photon interference experiments.

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Event by event method is a simulation approach which is not based on the knowledge of the Schrodinger equation. This approach uses the classical wave theory and particle concept: we use particles, not waves. The data is obtained by counting the events that were detected by the detector, just as in real experiments. The particle is considered as a messenger (carries a message) that is processed by the deterministic learning machine. We demonstrated that the event-based deterministic learning machine simulation can produce the same interference patterns as those obtained in the experiment. The event-by-event method reproduces the results of quantum theory of the Mach-Zehnder interferometer, Mach-Zehnder interferometer with absorber, three beam interference, delayed choice and two-photon interference experiments.
We propose and analyse simple deterministic algorithms that can be used to construct machines that have primitive learning capabilities. We demonstrate that locally connected networks of these machines can be used to perform blind classification on an event-by-event basis, without storing the information of the individual events. We also demonstrate that properly designed networks of these machines exhibit behavior that is usually only attributed to quantum systems. We present networks that simulate quantum interference on an event-by-event basis. In particular we show that by using simple geometry and the learning capabilities of the machines it is possible to simulate single-photon interference in a Mach–Zehnder interferometer. The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach–Zehnder interferometer. To illustrate that networks of these machines are indeed capable of simulating quantum interference we simulate, event-by-event, a setup involving two chained Mach–Zehnder interferometers, and demonstrate that also in this case the simulation results agree with quantum theory.
A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.
A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.
A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is presented. The event-based corpuscular model is shown to give a unified description of multiple-beam fringes of a plane parallel plate, single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum erasers, two-beam interference, double-slit, and Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments.
We analyze a single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable xxx, for each passage of a particle through the interferometer. Quantum theory predicts an interference pattern that is independent of the sequence of the values of xxx. On the other hand, corpuscular models that reproduce the results of quantum optics experiments carried out up to this date show a reduced visibility and a shift of the interference pattern depending on the details of the sequence of the values of xxx. The proposed experiment will show that: (1) it can be described by quantum theory, and thus not by the current corpuscular models, or (2) it cannot be described by quantum theory but can be described by the corpuscular models or variations thereof, or (3) it can neither be described by quantum theory nor by corpuscular models. Therefore, the proposed experiment can be used to determine to what extent quantum theory provides a description of observed events beyond the usual statistical level.