Correlations and entanglement in probability theory
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.
Cite
@article{arxiv.quant-ph/0211083,
title = {Correlations and entanglement in probability theory},
author = {E. G. Beltrametti and S. Bugajski},
journal= {arXiv preprint arXiv:quant-ph/0211083},
year = {2007}
}
Comments
10 pages, Latex, corrected typos