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arXiv:quant-ph/0511261

Possibly novel demonstration of nonlocality for two maximally entangled particles

Demetrios A. Kalamidas

Published Nov 29, 2005• 0 citations
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Abstract

We present, at the gedanken level, a possibly novel non-statistical demonstration of nonlocality for two maximally entangled particles. The argument requires only two alternative experimental contexts, only one and the same single-particle observable, and leads to a contradiction with a constrained form of local realism in 50% of experimental runs. However, the argument is based on a 'plausible' but not definitive notion of locality.

DOI
10.48550/arxiv.quant-ph/0511261

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We present, at the gedanken level, a possibly novel non-statistical demonstration of nonlocality for two maximally entangled particles. The argument requires only two alternative experimental contexts, only one and the same single-particle observable, and leads to a contradiction with a constrained form of local realism in 50% of experimental runs. However, the argument is based on a 'plausible' but not definitive notion of locality.
In a recent article [Phys. Rev. A 53, R1927 (1996)] Wu et al. give a proof of nonlocality for the maximally entangled state of two particles without using inequalities. Here we point out that in order for their argument to go through it is necessary to consider a minimum total of six dimensions in Hilbert space. Indeed, the above argument is found to fail whenever the dimensionality of the product Hilbert space is reduced to four. The explanation for this failure is provided by the fact according to which no direct contradiction between the quantum-mechanical and locally realistic predictions can arise for any fraction of an ensemble of 2\ifmmode\times\else\texttimes\fi{}2 systems configured in the maximally entangled state.
Many experiments have shown that locality-realism theory is at variance with quantum mechanics predictions. Although locality and realism, which are two different conceptions, are given respective definition, the descriptions of the both are a little of abstract when they are applied to real experimental situations. The abstract descriptions result in difficulty for one to judge whether the variance come from locality or realism or both. Here we provide more detailed descriptions of locality and realism, and show that any system being in a pure state or a non-maximally mixed state has property of non-realism. We also present experimental schemes feasible under current technologies to test the non-locality realsim. The connections between non-locality and entanglement and correlation are also discussed.
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We provide a streamlined proof of Hardy's theorem, that almost every entangled state for a pair of quantum particles admits a ``proof of nonlocality'' without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy's assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.