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EPJ Web of Conferences

Revealing violations of macrorealism in flavor oscillations: Leggett-Garg inequalities and no-signaling-in-time conditions

Massimo Blasone A, Fabrizio Illuminati, Luciano Petruzziello, Kyrylo Simonov, L. A. Smaldone

Published Jan 1, 2024• 0 citations
Publisher

Abstract

Abstract. We briefly review recent developments in the study of the quantum nature of flavor mixing; in particular, the attention will be devoted to neutrino and neutral meson oscillations. We employ Leggett-Garg type inequalities and no-signaling-in-time conditions to probe the intrinsic quantumness of such a physical manifestation, showing how the analysis is not affected by the wave-packet spreading (for neutrinos) and the intrinsic particle instability (for mesons).

DOI
10.1051/epjconf/202429103001

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Abstract. We briefly review recent developments in the study of the quantum nature of flavor mixing; in particular, the attention will be devoted to neutrino and neutral meson oscillations. We employ Leggett-Garg type inequalities and no-signaling-in-time conditions to probe the intrinsic quantumness of such a physical manifestation, showing how the analysis is not affected by the wave-packet spreading (for neutrinos) and the intrinsic particle instability (for mesons).
Abstract We consider two necessary and sufficient conditions for macrorealism recently appeared in the literature, known as no-signaling-in-time and arrow-of-time conditions, respectively, and study them in the context of neutrino flavor transitions, within both the plane wave description and the wave packet approach. We then compare the outcome of the above investigation with the implication of various formulations of Leggett–Garg inequalities. In particular, we show that the fulfillment of the addressed conditions for macrorealism in neutrino oscillations implies the fulfillment of the Leggett–Garg inequalities, whereas the converse is not true. Finally, in the framework of wave packet approach, we also prove that, for distances longer than the coherence length, the no-signaling-in-time condition is always violated whilst the Leggett–Garg inequalities are not.
Macrorealism is a fundamental concept in quantum foundations, capturing basic features of our everyday experience. Among the main tools introduced to test violations of macrorealism are the Leggett-Garg inequalities. These inequalities provide necessary and sufficient conditions for a certain data set including the correlators measured in a number of different experimental runs (weak version of macrorealism). Leggett-Garg inequalities have proved useful for detecting violations of macrorealism in neutrino oscillation experiments. However, it is interesting to investigate a set of necessary and sufficient conditions for strong macrorealism - no-signaling-in-time and arrow-of-time conditions - in order to obtain a more complete characterization of macrorealism in the context of neutrino oscillations. In particular, here we extend previous study of the no-signaling-in-time condition to the case of three-flavor neutrino oscillations, including the CP-violating phase of the Pontecorvo-Maki-Nakagawa-Sakata matrix.
Macrorealism formalizes the seemingly intuitive notion that, in contrast with the principles of quantum mechanics, a physical system can be in a definite state at any given time and moreover its dynamical evolution is independent of the measurements performed on it. In this study, we carry out a comparative analysis between three-time Leggett--Garg-type inequalities and the conditions of no-signaling-in-time and arrow-of-time for macrorealism within the context of meson oscillations. Our findings indicate that, under given initial conditions, no violations of Leggett--Garg inequalities are observed. However, no-signaling-in-time conditions are found to be violated, thereby revealing the impossibility of applying a macrorealistic description to the physics of meson oscillations.
The correlations between successive measurements of a quantum system can violate a family of Leggett-Garg Inequalities (LGIs) that are analogous to the violation of Bell’s inequalities of measurements performed on spatially separated quantum systems. These LGIs follow from a point of view, imposing that a classical system is at all times in a definite state and that a measurement can, at least in principle, leave this state undisturbed. Violations of LGIs can be probed by neutrino flavor oscillations if the correlators of consecutive flavor measurements are approximately stationary. We discuss here several improvements of the methodology used in previous analyses based on accelerator and reactor neutrino data. We argue that the strong claims of LGI violations made in previous studies are based on an unsuitable modeling of macrorealistic systems in statistical hypothesis tests. We illustrate our improved methodology via the example of the MINOS muon-neutrino survival data, where we find revised statistical evidence for violations of LGIs at the ( 2 – 3 ) σ level, depending on macrorealistic background models.
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.