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arXiv · 0705.1385

Bell inequalities for continuous-variable correlations

E. G. Cavalcanti·C. J. Foster·M. D. Reid·P. D. Drummond
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Abstract

We derive a new class of correlation Bell-type inequalities. The inequalities are valid for any number of outcomes of two observables per each of n parties, including continuous and unbounded observables. We show that there are no first-moment correlation Bell inequalities for that scenario, but such inequalities can be found if one considers at least second moments. The derivation stems from a simple variance inequality by setting local commutators to zero. We show that above a constant detector efficiency threshold, the continuous variable Bell violation can survive even in the macroscopic limit of large n. This method can be used to derive other well-known Bell inequalities, shedding new light on the importance of non-commutativity for violations of local realism.

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E. G. Cavalcanti, C. J. Foster, M. D. Reid, P. D. Drummond. 2007-11-24. Bell inequalities for continuous-variable correlations. https://doi.org/10.1103/physrevlett.99.210405

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