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International Journal of Quantum Information

TESTS OF QUANTUM MECHANICS AGAINST A SIMPLE FAMILY OF LOCAL HIDDEN-VARIABLES MODELS VIA POLARIZATION CORRELATION EXPERIMENTS

Emilio Santos

Published Jan 1, 2009• 0 citations
Publisher

Abstract

The quantum prediction for the polarization correlation of a general two-photon state (e.g. non-maximally entangled) is derived taking into account the non-ideal behavior of polarization analyzers and detectors. A simple family of local hidden-variables models is defined and the possible discrimination between that family and quantum mechanics is discussed.

DOI
10.1142/s0219749909004864

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The quantum prediction for the polarization correlation of a general two-photon state (e.g. non-maximally entangled) is derived taking into account the non-ideal behavior of polarization analyzers and detectors. A simple family of local hidden-variables models is defined and the possible discrimination between that family and quantum mechanics is discussed.
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An analysis is made of the results of a recent polarization correlation experiment by Bovino (unpublished) where about 60,000 data have been obtained. I assume that the state of the photon pairs produced in the source (a non-linear crystal) are in a (slightly)non-maximally entangled state and the most relevant non-idealities of the set-up are taken into account. A comparison is made between the predictions of quantum mechanics and a simple family of local hidden varaibles models with the result that the former is violated by more than 4 standard deviations whislt the data are compatible with the family of local models.
A family of theories called "deterministic local hidden variable theories" (DLHV) is characterized and their consequences are investigated for an experimentally realistic situation. An experiment on the polarization correlation of optical photon pairs emitted in certain atomic cascades is proposed as a test of the family of DLHV theories. The model-independent hidden variable predictions applicable to the realistic experimental arrangement are obtained by a generalization of a previous theorem of Bell. Quantum mechanical predictions for the same experimental situation are calculated for two cases: a J = 0 + J = 1 + J = 0 and a J = 1 + J = 1 + J = 0 electric dipole cascade. For both cascades, it is shown that the quantum mechanical and the DLHV predictions are in sufficient disagreement for an actual experimental test to be possible. Restrictions on detector solid angle and polarizer efficiency, necessary to obtain a decisive experiment, are explicitly given. The Einstein, Podolsky, and Rosen argument for the existence of a DLHV theory is reviewed.
Abstract We propose a novel class of local deterministic models to explain the correlations observed in entangled singlet quantum states. In these models, hidden variables influence both the entangled pair preparation and the measurement settings, thereby relaxing the measurement independence assumption used in Bell’s theorem. Our model accurately reproduces the expected quantum results and demonstrates that freely chosen measurement settings do not necessarily preclude the possibility of hidden variables inducing correlations between the settings and outcomes. This approach reveals an intricate relationship between local determinism and quantum mechanics, showing that local hidden variable theories can be consistent with the predictions of quantum theory. This result calls into question the conventional interpretation, based on Bell’s inequalities, that local theories are fundamentally incompatible with quantum mechanics.