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arXiv:1908.03924 · Frontiers in Physics

Local Realistic Interpretation of Entangled Photon Pairs in the Weyl-Wigner Formalism

Emilio Santos

Published Jun 3, 2020• 13 citations
arXivHTMLPDF

Abstract

A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl-Wigner formalism, that reproduces the quantum predictions. A realistic stochastic interpretation is proposed suggesting that an analysis of the experiments more detailed than the Bell approach may be compatible with local realism. Entanglement appears as a correlation between fluctuations of signal and vacuum fields.

DOI
10.3389/fphy.2020.00191

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A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl-Wigner formalism, that reproduces the quantum predictions. A realistic stochastic interpretation is proposed suggesting that an analysis of the experiments more detailed than the Bell approach may be compatible with local realism. Entanglement appears as a correlation between fluctuations of signal and vacuum fields.
We characterize the electromagnetic vacuum as a stochastic field. Some consequences, like the particle behaviour of light, are studied. The stochastic approach is connected with the standard Hilbert space formalism via the Weyl transform. Several experiments involving spontaneous parametric down conversion are studied comparing Hilbert space and Weyl–Wigner formalisms. This allows an intuitive picture of entanglement to be obtained as a correlation between field fluctuations in distant places, involving the vacuum fields. The analysis shows that the Bell definition of local realism is not general enough, whence the reported violation of Bell inequalities does not refute local realism.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward "subtraction" of the average ZPF intensity at the Wigner image of the detection process.
Abstract I revisit the Wigner (or Weyl–Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which turns out to be (classical) Maxwell theory with the assumption that there is a random radiation filling space, the vacuum field. I elucidate why, in sharp contrast, non-relativistic quantum mechanics of particles does not admit a realistic interpretation via WW. I interpret experiments involving entangled light beams within WW, in particular optical tests of Bell inequalities. I show that WW provides clues in order to construct local models for those experiments. I give arguments why Bell definition of local realism is not general enough.
In recent years parametric-down-conversion photon sources have been proposed and used to test local realism via Bell-type inequalities. This study shows that this technique fails to discriminate between quantum mechanics and local realism in all those tests in which polarization correlations are measured, since dichotomic observables cannot be associated satisfactorily with the state produced in these experiments. A more adequate description of these photon sources leads to an alternative inequality for Einstein locality, which is always satisfied by quantum-mechanical predictions. The result can be extended to all the experiments in which only one-half of the emitted pairs are detected.