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arXiv:quant-ph/9812053

Two-photon Franson-type interference experiments are not tests of local realism

Jan-Åke Larsson, Sven Aerts, Marek Żukowski

Published Dec 18, 1998• 2 citations
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Abstract

We report a local hidden-variable model which reproduces quantum predictions for the two-photon interferometric experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)]. The model works for the ideal case of full visibility and perfect detection efficiency. This result changes the interpretation of a series of experiments performed in the current decade.

DOI
10.48550/arxiv.quant-ph/9812053

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We report a local hidden-variable model which reproduces quantum predictions for the two-photon interferometric experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)]. The model works for the ideal case of full visibility and perfect detection efficiency. This result changes the interpretation of a series of experiments performed in the current decade.
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.
We report on a two-photon interference experiment proposed by Franson [Phys. Rev. Lett. 62, 2205 (1989)], in which sinusoidal fringes with visibilities greater than 70.7%, such as those predicted by quantum mechanics, violate a Bell inequality. We observe visibility of 80.4\ifmmode\pm\else\textpm\fi{}0.6%, implying a violation of the inequality by 16 standard deviations. Here the elements of reality under consideration are energy and time rather than spin components. Any classical field models describing separate beams in a Franson interferometer are limited to visibilities less than 50%, and hence ruled out as well, without the need for any supplementary assumptions.
A local hidden-variable model is exhibited for the experiments by Aspect, Grangier, and Roger [Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982)] and Aspect, Dalibard, and Roger [Phys. Rev. Lett. 49, 1804 (1982)] measuring polarization correlation of optical-photon pairs. The model agrees with quantum-mechanical predictions for all measurable quantities even with ideal polarizers and detectors, and emphasizes the need of a high degree of directional correlation, besides the correlation of spin (or polarization or other quantities), in any test of locality. It is proved that homogeneous inequalities, involving only coincidence detection rates, cannot discriminate between quantum mechanics and local theories, which invalidates all previously used empirical tests. The role of supplementary assumptions, like the so-called no enhancement, for the derivation of Bell's inequalities is discussed. Finally it is conjectured that quantum mechanics might be compatible with local realism, if we assume that not all self-adjoint operators represent observables and not all density operators represent states.
An experiment has recently been performed to demonstrate quantum nonlocality by establishing contextuality in one of a pair of photons encoding four qubits; however, low detection efficiencies and use of the fair-sampling hypothesis leave these results open to possible criticism due to the detection loophole. In this Letter, a physically motivated local hidden-variable model is considered as a possible mechanism for explaining the experimentally observed results. The model, though not intrinsically contextual, acquires this quality upon post-selection of coincident detections. • A local hidden-variable model is applied to a recent quantum optics experiment. • The experiment was designed to demonstrate quantum nonlocality via local contextuality. • Using a single fitting parameter, the model accurately predicts the observed results.