

Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
December 25, 2014 11:00, Moscow, Steklov Mathematical Institute of RAS, Room 430 (8 Gubkina)






CHSH inequality: Quantum probabilities as classical conditional probabilities
A. Yu. Khrennikov^{} 
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Abstract:
The theorem of A. Fine implies that the CHSH inequality (the
experimentally testable version of the famous Bell inequality) is violated
if and only if the joint probability distribution for the quadruples of
observables involved the EPR–Bohm–Bell experiment does not exist, i.e., it
is impossible to use the classical probabilistic model (Kolmogorov, 1933).
We demonstrate that, in spite of Fine's theorem, the results of
observations in the Bell experiment can be described in the classical
probabilistic framework. However, the “quantum probabilities” have to be
interpreted as conditional probabilities, where conditioning is with
respect to fixed experimental settings. Our approach is based on the
complete account of randomness involved in the experiment. The crucial
point is that randomness of selections of experimental settings has to
be taken into account. This approach can be applied to any complex
experiment in which statistical data are collected for various (in general
incompatible) experimental settings.
Language: English
References

A. Khrennikov, CHSH inequality: Quantum probabilities as classical conditional probabilities, arXiv: 1406.4886

