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Springer eBooks

Violations of Local Realism in a Hardy-Jordan-Type Experiment Without Use of Bell Inequalities

David A. Branning, J. R. Torgerson, Carlos Henrique Monken, L. Mandeļ

Published Jan 1, 1996• 0 citations
Publisher
DOI
10.1007/978-1-4757-9742-8_201

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We have performed a test of local realism using entangled photons produced by spontaneous parametric downconversion. This experimental test is based on an idea originally proposed by Hardy for a test of local realism without inequalities, although our experiment actually measures an inequality (as any experiment must). We find a more-than-70 standard deviation violation of the predictions of local realism. The experimental effort required for this test is essentially the same as that required for a test of a Bell inequality. However, this test is based on concepts that are easier to understand and more compelling than those behind the original Bell inequality.
Nonlocality without inequality is an elegant argument introduced by Hardy for two qubit systems, and later generalised to n qubits, to establish contradiction of quantum theory with local realism. Interestingly, for n = 2 this argument is actually a corollary of Bell-type inequalities, viz., the CH–Hardy inequality involving Bell correlations, but for n greater than two it involves n-particle probabilities more general than Bell-correlations. In this paper, we first derive a chain of completely new local realistic inequalities involving joint probabilities for n qubits and then associated with each such inequality, we provide a new Hardy-type local reality constraint without inequalities. Quantum mechanical maximal violations of the chain of inequalities and of the associated constraints are also studied by deriving appropriate Cirel'son-type theorems. These results involving joint probabilities more general than Bell correlations are expected to provide a new systematic tool to investigate entanglement.