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Correlations and entanglement in probability theory

E. G. Beltrametti·S. Bugajski
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Abstract

We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion of probabilistic correlation and show that it includes two kinds of correlation: a classical one, which occurs for both deterministic and indeterministic observables, and a nonclassical one, which occurs only for indeterministic observables. The latter will be called probabilistic entanglement and represents a property of intrinsically random systems, not necessarily quantum. It appears possible to separate the two kinds of correlation and characterize them by numerical functions which satisfy a simple product rule.

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E. G. Beltrametti, S. Bugajski. 2003-10-17. Correlations and entanglement in probability theory. https://arxiv.org/abs/quant-ph/0211083

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