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Correlations and Entanglement in Probability Theory

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Abstract

We generalize the classical probability frame by adopting a wider family of random variables that includes non-deterministic 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 non-classical 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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Authors and Affiliations

  1. Department of Physics, University of Genoa, INFN-Sezione di Genova, Via Dodecaneso 33, Genova, Italy, I-16146

    E. G. Beltrametti

  2. Institute of Physics, University of Silesia, Katowice, Poland

    S. Bugajski

  3. Institute of Pure and Applied Computer Science, Polish Academy of Sciences, al. Lotników 32/46, Warszawa, Poland, 02-668

    S. Bugajski

  4. Department of Physics, University of Genoa, INFN-Sezione di Genova, Via Dodecaneso 33, Genova, Italy, I-16146

    E. G. Beltrametti

Authors
  1. E. G. Beltrametti
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  2. S. Bugajski
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Correspondence to E. G. Beltrametti.

Additional information

This paper was written a few months before the death of S. Bugajski: the first author recalls him as a creative scientist, a great human personality, and a dear friend.

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Beltrametti, E.G., Bugajski, S. Correlations and Entanglement in Probability Theory. Int J Theor Phys 44, 827–837 (2005). https://doi.org/10.1007/s10773-005-7061-z

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  • DOI: https://doi.org/10.1007/s10773-005-7061-z

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