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arXiv:quant-ph/9912064 · Physical Review Letters

Two-Photon Franson-Type Experiments and Local Realism

Sven Aerts, Paul G. Kwiat, Jan-Åke Larsson, Marek Żukowski

Published Oct 11, 1999• 100 citations
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Abstract

The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a ``Bell test of local realism.'' However, it has been suggested that this is incorrect due to the $50%$ postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.

DOI
10.1103/physrevlett.83.2872

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The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a ``Bell test of local realism.'' However, it has been suggested that this is incorrect due to the 5050%50 postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.
Several recent papers have shown that some forms of dispersion cancellation have classical analogs and that some aspects of nonlocal two-photon interferometry are consistent with local realistic models. It is noted here that the classical analogs only apply to local dispersion cancellation experiments [A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 68, 2421 (1992)] and that nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A 45, 3126 (1992)] is inconsistent with any classical field theory and has no classical analog. The local models that have been suggested for two-photon interferometry are shown to be local but not realistic if the spatial extent of the interferometers is taken into account. It is the inability of classical models to describe all of the relevant aspects of these experiments that distinguishes between quantum and classical physics, which is also the case in Bell's inequality.
The Franson interferometer, proposed in 1989 (Franson 1989 Phys. Rev. Lett. 6 2 2205–08 ), beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experiments and Einstein–Podolsky–Rosen (EPR) elements of reality. The mentioned sinusoidal interference pattern is the same as that giving a violation in the usual Bell experiment. Even so, depending on the precise requirements made on the local realist model, this can imply (a) no violation, (b) smaller violation than usual, or (c) full violation of the appropriate statistical bound. Alternatives include (a) using only the measurement outcomes as EPR elements of reality, (b) using the emission time as EPR element of reality, (c) using path realism, or (d) using a modified setup. This paper discusses the nature of these alternatives and how to choose between them. The subtleties of this discussion needs to be taken into account when designing and setting up experiments intended to test local realism. Furthermore, these considerations are also important for quantum communication, for example in Bell-inequality-based quantum cryptography, especially when aiming for device independence. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
In a recent article Giustina et al. [Phys. Rev. Lett. 115, 250401 (2015)] report on an advanced Bell experiment, simultaneously closing loopholes for local hidden-variable theories. The authors claim that 'local realism' has been refuted, unless 'truly exotic hypotheses' are made. Here I argue that a particularly wide and natural class of local hidden-variable theories survives, for instance when the hidden variables describe a background field. Such background-based theories exploit the freedom-of-choice loophole, which cannot be closed for this type of hidden variables. The dynamics of such models can be illustrated by existing systems, e.g. from fluid mechanics.