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arXiv:2111.09979 · Physical Review A

Leggett-Garg inequalities in the quantum field theory of neutrino oscillations

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

Published Sep 14, 2023• 24 citations
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Abstract

We investigate Leggett-Garg inequalities for neutrino oscillations in the quantum field theoretical setting. We derive an exact flavor-mass uncertainty relation and prove that this uncertainty product yields an upper bound to the violation of the inequalities. The relation between temporal nonclassicality and quantum uncertainty realizes the L\"uders upper bound to the violation of the Leggett-Garg inequalities in quantum field theory, analogous to the Tsirelson upper bound to the violation of the Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that on average the inequalities are violated more often and more strongly in quantum field theory than in quantum mechanics.

DOI
10.1103/physreva.108.032210

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We investigate Leggett-Garg inequalities for neutrino oscillations in the quantum field theoretical setting. We derive an exact flavor-mass uncertainty relation and prove that this uncertainty product yields an upper bound to the violation of the inequalities. The relation between temporal nonclassicality and quantum uncertainty realizes the L"uders upper bound to the violation of the Leggett-Garg inequalities in quantum field theory, analogous to the Tsirelson upper bound to the violation of the Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that on average the inequalities are violated more often and more strongly in quantum field theory than in quantum mechanics.
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.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6 σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. The weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett–Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a 6.1σ6.1\sigma 6.1σ significance of the violation of them.
The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour (νeL↔νμLν_{e}^{L}\leftrightarrowν_μ^{L}νeL​↔νμL​) and spin (νeL↔νeRν_{e}^{L}\leftrightarrowν_{e}^{R}νeL​↔νeR​) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions ΔLΔLΔL where the LGI is violated, as quantified by the correlator functions K3K_{3}K3​ and K4K_{4}K4​.
Neutrino oscillation represents an intriguing physical phenomenon where the quantumness can be maintained and detected over a long distance. Previously, the nonclassical character of neutrino oscillation was tested with the Leggett-Garg inequality, where a clear violation of the classical bound was observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)]. However, there are several limitations in testing neutrino oscillations with the Leggett-Garg inequality. In particular, the degree of violation of the Leggett-Garg inequality cannot be taken as a ``measure of quantumness.'' Here, we focus on quantifying the quantumness of experimentally observed neutrino oscillation, using the tools of the recently developed quantum resource theory. We analyzed ensembles of reactor and accelerator neutrinos at distinct energies from a variety of neutrino sources, including Daya Bay (0.5 and 1.6 km), KamLAND (180 km), MINOS (735 km), and T2K (295 km). The quantumness of the three-flavored neutrino oscillation is characterized within a $3\ensuremath{\sigma}$ range relative to the theoretical prediction. It is found that the maximal coherence was observed in the neutrino source from the KamLAND reactor. However, even though the survival probability of the Daya Bay experiment did not vary significantly (it dropped about 10%), the coherence recorded can reach up to 40% of the maximal value. These results represent the longest distance over which quantumness was experimentally determined for quantum particles other than photons.