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Entropy, Vol. 20, Pages 500: On the Significance of the Quantum Mechanical Covariance Matrix

Entropy, Vol. 20, Pages 500: On the Significance of the Quantum Mechanical Covariance Matrix

Entropy doi: 10.3390/e20070500

Authors: Avishy Carmi Eliahu Cohen

The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work, we show that the extent of binary correlations in a general class of nonlocal theories can be characterized by the existence of a certain covariance matrix. The set of quantum realizable two-point correlators in the bipartite case then arises from a subtle restriction on the structure of this general covariance matrix. We also identify a class of theories whose covariance has neither a quantum nor an “almost quantum” origin, but which nevertheless produce the accessible two-point quantum mechanical correlators. Our approach leads to richer Bell-type inequalities in which the extent of nonlocality is intimately related to a non-additive entropic measure. In particular, it suggests that the Tsallis entropy with parameter q=1/2 is a natural operational measure of non-classicality. Moreover, when generalizing this covariance matrix, we find novel characterizations of the quantum mechanical set of correlators in multipartite scenarios. All these predictions might be experimentally validated when adding weak measurements to the conventional Bell test (without adding postselection).

Authors:   Carmi, Avishy ; Cohen, Eliahu
Journal:   Entropy
Volume:   20
edition:   7
Year:   2018
Pages:   500
DOI:   10.3390/e20070500
Publication date:   28-Jun-2018
Facts, background information, dossiers
  • quantum
  • Matrix
  • entropy
  • Bell
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