Scientific article
Open access

Covariance Bell inequalities

Published inPhysical Review. A, vol. 96, no. 062128
Publication date2017

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Citation (ISO format)
POZSGAY, Victor et al. Covariance Bell inequalities. In: Physical Review. A, 2017, vol. 96, n° 062128. doi: 10.1103/PhysRevA.96.062128
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Article (Accepted version)
ISSN of the journal1050-2947

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