Bell inequalities for continuous-variable correlations
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.
Keywords
Cite
@article{arxiv.0705.1385,
title = {Bell inequalities for continuous-variable correlations},
author = {E. G. Cavalcanti and C. J. Foster and M. D. Reid and P. D. Drummond},
journal= {arXiv preprint arXiv:0705.1385},
year = {2007}
}