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Quantum Information and Computation

Generalized Bell inequalities with parametric down-conversion

Antı́a Lamas-Linares, William T. M. Irvine, John C. Howell, Dirk Bouwmeester

Published Oct 1, 2003• 0 citations
Publisher

Abstract

We analize the suitability of states generated by stimulated parametric down-conversion for the testing of high dimensional Bell-type inequalities. Two families of bipartite inequalities are considered. For both it is found that the states are good candidates for the tests and some experimental results for one spin-1 inequality are given. The influence of noise and the possibility of supurious results are discussed.

DOI
10.26421/qic3.s-2

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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.

Physical Review A•Oct 1, 1995•13 citations
We analize the suitability of states generated by stimulated parametric down-conversion for the testing of high dimensional Bell-type inequalities. Two families of bipartite inequalities are considered. For both it is found that the states are good candidates for the tests and some experimental results for one spin-1 inequality are given. The influence of noise and the possibility of supurious results are discussed.
We show that various experimental configurations using correlated photon-number states are predicted to violate many forms of Bell's inequality. This test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where large numbers of photons are detected at a single detector at a time. The configurations also allow higher-spin tests of quantum mechanics. We indicate how the violations of Bell inequalities might be achieved with both parametric amplification and parametric oscillation. The effect of photodetection inefficiencies is analyzed. In order to investigate the potential for Bell-inequality tests in the high-intensity regime of recent experiments where detection efficiencies may be very high, we introduce a simple model for the effect of electronic noise that introduces a poor resolution of the photon number detected.
We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini et al. The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.
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.