Test of a hypothesis of realism in quantum theory using a Bayesian approach

Abstract

In this paper we propose a time-independent equality and time-dependent inequality, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional probability and on Bayes' theorem in the framework of Kolmogorov's axiomatics of probability theory. The equality obtained is intrinsically different from the well known GHZ-equality and its variants, because violation of the new equality might be tested in experiments with only two microsystems in a maximally entangled Bell state | Ψ − ⟩, while a test of the GHZ-equality requires at least three quantum systems in a special state | Ψ GHZ ⟩. The obtained inequality differs from Bell's, Wigner's, and Leggett-Garg inequalities, because it deals with spin = 1/2 projections onto only two non-parallel directions at two different moments of time, while a test of the Bell and Wigner inequalities requires at least three non-parallel directions, and a test of the Leggett-Garg inequalities -at least three distinct moments of time. Hence, the proposed inequality seems to allow one to avoid the "contextuality loophole". Violation of the proposed equality and inequality is illustrated with the behaviour of a pair of anti-correlated spins in an external magnetic field and also with the oscillations of flavour-entangled pairs of neutral pseudoscalar mesons.

Wigner inequalities for testing the hypothesis of realism and concepts of macroscopic and local realism

“…violation of ( 25) may be considered in κ " 0 regime. In this case inequality (25) (26), and consequently to violation of inequality (21). We have shown that inequality( 21) may be violated in quantum theory.…”

“…In references [22,23,24] some attempts have been made to obtain a non-stationary version of the Wigner inequalities in the framework of local realism. In [25] another attempt has been made: using the Bayes theorem and its combination with hypothesis of realism. The results of these studies have demonstrated that the description of testing of quantum concepts in the "probabilistic approach" (which is based on ideas of Wigner) has potential comparable to the commonly used "orthodox" correlator-based approach.…”

“…This paper is a continuation of series of papers studying time-dependent extensions of the Wigner inequalities [22,23,24,25]. This series was stimulated by a desire to generalize the Bell inequalities [10,11,12] and Wigner inequalities [9] for quantum field theory (QFT).…”