Quantum correlations in neutrino oscillations in curved spacetime

Abstract

Gravity induced neutrino-antineutrino oscillations are studied in the context of one and two flavor scenarios. This allows one to investigate the particle-antiparticle correlations in two and four level systems, respectively. Flavor entropy is used to probe the entanglement in the system. The well known witnesses of non-classicality such as Mermin and Svetlichly inequalities are investigated. Since the extent of neutrino-antineutrino oscillation is governed by the strength of the gravitational field, the behavior of non-classicality shows interesting features as one varies the strength of the gravitational field. Specifically, the suppression of the entanglement with the increase of the gravitational field is observed which is witnessed in the form of decrease in the flavor entropy of the system. The features of the Mermin and the Svetlichny inequalities allow one to make statements about the degeneracy of neutrino mass eigenstates.

Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

“…As is the case in the Poincaré sphere of a single spin−1/2 particle, the above equation suggests that α and β parameterize a two-sphere called Schmidt sphere. Note that various quantum correlations of the system of basic one-flavor and two-flavor neutrino and antineutrino states in the presence of gravitational field and hence gravitational Zeeman splitting, as described in Section 3, were already explored by one of the present authors [34]. Flavor entropy has been used therein to probe the entanglement in the system, which gets suppressed with the increase of gravitational field.…”

“…Dirac equation in the presence of background gravitational fields has already been shown to have many consequences (see, e.g., the work by one of the present authors [25,26,28,33,34]) and is known to have the form (see, e.g., [26,[34][35][36])…”

“…Figure 2 represents the energy splitting given by Equation (11), which was already introduced briefly by one of us [34,40] (note, however, a typo in the notation of the first splitting in those works).…”

“…where E ψ and E ψ c are dispersion energies of neutrino and anti-neutrino respectively, in local coordinates neglecting their variation, given by (see also, e.g., [34])…”

Non-uniform magnetic field as a booster for quantum speed: faster quantum information processing

“…In recent times, the cross-fertilization of quantum information ideas with relativistic quantum mechanics has been particularly fruitful. Thus, for example, this has impacted developments in Leggett-Garg inequalities [22,23], probes of curved spacetime [24], geometric phase [25] and coherence [26] in the context of subatomic particles, such as, neutrinos and neutral mesons. This approach has also led to investigations into the Unruh effect [27].…”