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arXiv:1906.05995 · Journal of Physics G Nuclear and Particle Physics

Probing inequivalent forms of Leggett–Garg inequality in subatomic systems

Javid Naikoo, Swati Kumari, Subhashish Banerjee, A K Pan

Published Jun 24, 2020• 13 citations
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Abstract

Abstract We study various formulations of Leggett–Garg inequality (LGI), specifically, the Wigner and Clauser–Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as well as meson systems. The optimal forms of various LGIs for either neutrinos or mesons are seen to depend on measurement settings. For the neutrinos, some of these inequalities can be written completely in terms of experimentally measurable probabilities. Hence, the Wigner and Clauser–Horne forms of LGI are found to be more suitable as compared to the standard LGI from the experimental point of view for the neutrino system. Further, these inequalities exhibit maximum quantum violation around the energies roughly corresponding to the maximum neutrino flux. The Leggett–Garg type inequality is seen to be more suited for the meson dynamics. The meson system being inherently a decaying system allows one to see the effect of decoherence on the extent of violation of various inequalities. Decoherence is observed to reduce the degree of violation, and hence the nonclassical nature of the system.

DOI
10.1088/1361-6471/ab9f9b

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Abstract We study various formulations of Leggett–Garg inequality (LGI), specifically, the Wigner and Clauser–Horne forms of LGI, in the context of subatomic systems, in particular, three flavor neutrino as well as meson systems. The optimal forms of various LGIs for either neutrinos or mesons are seen to depend on measurement settings. For the neutrinos, some of these inequalities can be written completely in terms of experimentally measurable probabilities. Hence, the Wigner and Clauser–Horne forms of LGI are found to be more suitable as compared to the standard LGI from the experimental point of view for the neutrino system. Further, these inequalities exhibit maximum quantum violation around the energies roughly corresponding to the maximum neutrino flux. The Leggett–Garg type inequality is seen to be more suited for the meson dynamics. The meson system being inherently a decaying system allows one to see the effect of decoherence on the extent of violation of various inequalities. Decoherence is observed to reduce the degree of violation, and hence the nonclassical nature of the system.
Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral BdB_dBd​ , BsB_sBs​ and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter D[n]\mathscr {D}^{[n]}D[n] closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in BdB_dBd​ and BsB_sBs​ systems.
The present work is devoted to the characterization of the Leggett-Garg inequality (LGI) for three flavored neutrino oscillations in the presence of both matter and charge-conjugation and parity violating effects. This study complements and completes the recent one put forward in arXiv:1710.05562 by relaxing the stationary condition. At variance with the latter case, the LGI contains interference terms which cannot be expressed in terms of experimentally measurable quantities, thus drawing a clear-cut distinction between the two scenarios, as well as highlighting the role of the stationary assumption on such systems. We find that the additional terms are small for a high energy neutrino beam compared to the maximum value attained by the Leggett-Garg parameter.
Neutrinos, due to their weakly interacting nature, provide us with a unique opportunity to test foundations of quantum mechanics over macroscopic distances. There has been considerable theoretical and experimental interest in examining the extent of violation of Leggett-Garg inequalities (LGI) in the context of neutrino flavour oscillations. While it is established that neutrino oscillations occur due to mass and mixing among the three generations of neutrinos, sub-dominant effects due to physics beyond the Standard Model (SM) are not yet ruled out. As we are entering the precision era in neutrino physics, it is possible that some of these effects may leave an imprint on data. Thus, it is worthwhile to investigate different physics scenarios beyond the SM and study their impact on oscillation probabilities. In the present work, we invoke damping effects (including decoherence and decay) on oscillation probabilities and study their implications on the LGI.
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over 10σ10\sigma 10σ 10σ , and of over 90 %\%% % of theoretical predictions, while the KamLAND data exhibit violation of 1.9σ1.9\sigma 1.9σ 1.9σ , being of 58 %\%% % of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.
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.
Abstract Leggett Garg inequalities (LGIs) provides an elegant way for probing the incompatibility between the notion of macrorealism and quantum mechanics. For unitary dynamics the optimal quantum violation of a LGI is constrained by the L u ¨ ders bound. In this paper, we have studied two formulations of LGIs in three-time LG scenario, viz, the standard LGIs and third-order LGIs both for unbiased and biased measurement settings. We show that if system evolves under non-unitary quantum channel between two measurements, the quantum violations of both forms of LGIs exceed their respective L u ¨ ders bounds and can even reach their algebraic maximum in sharp measurement settings. We found that when the measurement is unsharp the quantum violations of both standard and third-order LGIs for non-unitary quantum channel can be obtained for lower value of the unsharpness parameter compared to the unitary dynamics. We critically examined the violation of L u ¨ ders bound of LGIs and its relation to the violation of various no-signaling in time conditions, another formalism for testing macrorealism. It is shown that mere violations of no-signaling conditions are not enough to warrant the violation of standard LGIs, an interplay between the violations of various NSIT condition along with a threshold value play an important role. On the other hand violation of third-order LGI is obtained when the degree of violation of a specific no-signaling in time condition reaches a different threshold value.