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Event-by-Event Simulation of Franson-Type Bell Experiments

Marcus Richter, Hans A. De Raedt, Kristel F. L. Michielsen

Published Aug 24, 2015• 0 citations
OpenAlex

Abstract

Abstract. Franson-Type Bell experiments have been proposed to demonstrate the violation of local realism in quantum theory based on a violation of the Bell Clauser-Horne-Shimony-Holt inequality. We demonstrate that the original experiment constructed by Franson [1] as well as its modification by Cabello et al. [2] can be simulated on an event-by-event basis using causal, local, and event-based processes without solving the Schrödinger equation or using concepts such as wave fields or particle-wave duality. In our approach networks of locally connected processing units with a primitive learning capability are used which exhibit behaviour that is usually only attributed to quantum systems. There is a one-to-one correspondence between the components of the network and the physical devices in the experimental setup. Furthermore, only simple geometry is used to construct the simulation algorithm. In this sense, the simulation approach we propose satisfies

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Abstract. Franson-Type Bell experiments have been proposed to demonstrate the violation of local realism in quantum theory based on a violation of the Bell Clauser-Horne-Shimony-Holt inequality. We demonstrate that the original experiment constructed by Franson [1] as well as its modification by Cabello et al. [2] can be simulated on an event-by-event basis using causal, local, and event-based processes without solving the Schrödinger equation or using concepts such as wave fields or particle-wave duality. In our approach networks of locally connected processing units with a primitive learning capability are used which exhibit behaviour that is usually only attributed to quantum systems. There is a one-to-one correspondence between the components of the network and the physical devices in the experimental setup. Furthermore, only simple geometry is used to construct the simulation algorithm. In this sense, the simulation approach we propose satisfies
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.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
Following an approach proposed by Eberhard, a graphical representation of entangled particles is used to provide insight into the meaning and direct experimental consequences of local realism. The most famous Bell-type theorems, like the original inequality developed by Bell, as well as the ones presented by Clauser, Horne, Shimony, and Holt, Clauser and Horn, Eberhard, d'Espagnat, and Maccone, are then derived by means of the graphical method. The universality and efficiency of the presented method in achieving different Bell's inequalities follow from making local realism explicitly a starting point in our general reasoning. The pedagogical and illustrative nature of the approach makes it easy to see directly how all the miscellaneous inequalities are actually rooted in the local realist view on microscopic particles.