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Physical Review A

Reliability of Bell-inequality measurements using polarization correlations in parametric-down-conversion photon sources

Liberato De, Augusto Garuccio

Published Oct 1, 1994• 50 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.r2803

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Comment on "Reliability of Bell-inequality measurements using polarization correlations in parametric-down-conversion photon sources"

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In a recent article [Phys. Rev. A 50, R2803 (1994)] De Caro and Garuccio state that many parametric-down-conversion sources cannot be used in tests of Bell's inequalities because they produce quantum-mechanical product states. Here we point out that not only have suitable sources already been proposed in the literature, but experiments not suffering from the problems cited by the authors have also been reported.

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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.
A certain class of parametric down-conversion Bell-type experiments has the following features. In the idealized perfect situation it is in only 50% of the cases that each observer receives a photon; in the other 5050%50 one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts about whether such experiments could ever be genuine tests of local realism. We propose to take into account these ``unfavorable'' cases and to analyze the entire pattern of polarization and localization correlations. This departure from the standard reasoning enables one to show that the experiments are indeed a true test of local realism.
In the last few years the parametric down-conversion of light has attracted the attention of the researchers in foundations of quantum physics. The photons that come out from the non-linear crystal are highly correlated in many variables. One of the most important consequences of entanglement is the possibility of violating the so called Einstein locality expressed in Bell's inequality. In general factorizable state vectors do not violate Bell's inequality, but we will show that the factorizable state vector produced with a beam-splitter set on the paths of parametric down-conversion photons violates a new inequality that can be deduced from local realism. This inequality is more stringent than those used up to now to test the locality.
John Bell’s theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell’s inequalities. Employing modifications of Bell’s inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.
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.
We report a new two-photon polarization correlation experiment for realizing the Einstein-Podolsky-Rosen-Bohm (EPRB) state and for testing Bell-type inequalities. We use the pair of orthogonally-polarized light quanta generated in Type 2 parametric down conversion. Using 1 nm interference filters in front of our detectors, we observe from the output of a 0.5mm beta - BaB2O4 (BBO) crystal the EPRB correlations in coincidence counts, and measure an associated Bell inequality violation of 22 standard deviations. The quantum state of the photon pair is a polarization analog of the spin-1/2 singlet state.