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arXiv:1411.5536 · Nuclear Physics B

Quantum correlations in terms of neutrino oscillation probabilities

Ashutosh Kumar Alok, Subhashish Banerjee, Sankagiri Uma Sankar

Published May 4, 2016• 93 citations
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Abstract

Neutrino oscillations provide evidence for the mode entanglement of neutrino mass eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent to consider the relation between the oscillation probabilities and other quantum correlations. In this work, we show that all the well-known quantum correlations, such as the Bell's inequality, are directly related to the neutrino oscillation probabilities. The results of the neutrino oscillation experiments, which measure the neutrino survival probability to be less than unity, imply Bell's inequality violation.

DOI
10.1016/j.nuclphysb.2016.05.001

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Neutrino oscillations provide evidence for the mode entanglement of neutrino mass eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent to consider the relation between the oscillation probabilities and other quantum correlations. In this work, we show that all the well-known quantum correlations, such as the Bell's inequality, are directly related to the neutrino oscillation probabilities. The results of the neutrino oscillation experiments, which measure the neutrino survival probability to be less than unity, imply Bell's inequality violation.
Neutrino oscillations provide evidence for the mode entanglement of neutrino mass eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent to ask if other quantum correlations are present in neutrino evolution. In this study, we compute a number of such correlations for accelerator neutrinos in the approximation of two flavour nu_{mu} nu_{tau} oscillations. The point of minimum survival probability corresponds to the extremum point of all measures of quantum correlations. We find that Bell's inequality is always violated.
Abstract In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the l 1 -norm as a coherence measure is equal to the sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by Blasone M. et al ., EPL , 112 (2015) 20007. Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of the l 1 -norm is investigated by varying the wave packet width . As expected, the amount of coherence increases by due to the increase in overlapping of the mass eigenstates.
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.
PACS 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell’s inequalities, GHZ states, etc.) PACS 03.67.Mn – Entanglement measures, witnesses, and other characterizations PACS 14.60.Pq – Neutrino mass and mixing Abstract – Flavor oscillations in elementary particle physics are related to multimode entan-glement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks. Copyright c © EPLA, 2009 Various branches of condensed matter, atomic physics,
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.
Abstract Non-local correlations in entangled systems are usually captured by measures such as Bell’s inequality violation. It was recently shown that in neutrino systems, a measure of non-local advantage of quantum coherence (NAQC) can be considered as a stronger measure of non-local correlations as compared to the Bell’s inequality violation. In this work, we analyze the effects of non standard interaction (NSI) on these measures in the context of two flavour neutrino oscillations for DUNE, MINOS, T2K, KamLAND, JUNO and Daya Bay experimental set-ups. We find that even in the presence of NSI, Bell’s inequality violation occurs in the entire energy range whereas the NAQC violation is observed only in some specific energy range justifying the more elementary feature of NAQC. Further, we find that NSI can enhance the violation of NAQC and Bell’s inequality parameter in the higher energy range of a given experimental set-up; these enhancements being maximal for the KamLAND experiment. However, the possible enhancement in the violation of the Bell’s inequality parameter over the standard model prediction can be up to 11% whereas for NAQC it is 7%. Thus although NAQC is a comparatively stronger witness of nonclassicality, it shows lesser sensitivity to NSI effects in comparison to the Bell’s inequality parameter.