Probing the Leggett-Garg inequality for oscillating neutral kaons and neutrinos

Abstract

The Leggett-Garg inequality (LGI) as a temporal analog of Bell's inequality, derived using the notion of realism, is studied in a hitherto unexplored context involving weak-interaction-induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of the LGI obtained from the relevant quantum mechanical results is significantly higher for oscillating neutrinos compared to that for kaons. Interestingly, the effect of CP noninvariance for the kaon oscillation is to enhance this violation, while, for neutrinos, the violation is sensitive to the value of mixing parameter.

Time-dependent Bell inequalities in a Wigner form

“…But it is obvious that the inequalities (18), (20), and (21) do not depend on α, as should be the case for any experimentally testable theory. Hence the static inequalities (4), written in terms of the oscillation parameters of neutral B-mesons (16), (19), are never violated, and do not allow testing of the complementarity principle.…”

“…nanomechanical resonators [17] may be used for such tests. Various generalizations of Leggett-Garg inequalities are actively discussed nowadays [18], as well as their possible applications to particle physics [19]. However none of the Leggett-Garg inequalities are suitable for tests of Bohr's complementarity principle;…”

Leggett-GargK3quantity discriminates between Dirac and Majorana neutrinos

“…(21) are formed by a very special combination of correlation functions C ij defined in Eq. (18). It is worth to mention that all the properties of the LG-correlators which seem to be useful for distinguishing Dirac and Majorana neutrinos essentially originate form the properties of C ij and ∆C ij = C ij (φ = 0) − C ij (φ) as presented in Fig.…”

Quantum contextuality of a single neutrino under interactions with matter

“…sin , cos , sin , for the angles α=π/5 and β=2π/5. Quantum non-locality of the Bell type related to quantum entanglement [28,29] and the one of the Leggett-Garg type [30][31][32] have been studied recently in a context of oscillating neutrino systems. In particular, [33] reports violation of the LGI in neutrino systems based upon the Main Injector Neutrino Oscillation Search experiment's data.…”