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The European Physical Journal C

Gravitational effects on quantum correlations in three-flavor neutrino oscillations

Guang-Jie Wang, Lijuan Li, Tao Wu, Xue‐Ke Song, Liu Ye, Dong Wang

Published Oct 30, 2024• 3 citations
Publisher

Abstract

Abstract In this paper, we explore the quantum properties of three-flavor neutrino propagating in a Schwarzschild metric. It is found that the different strength of gravitational effects are obtained by adjusting the magnitude of $$\mathrm GM$$ G M arising in the oscillation phase. Using the weak field approximations, we show that the gravitational effects can make the entanglement oscillates over a large rage when $$\textrm{GM}=5.1\times 10^8 \, \textrm{Km}$$ GM = 5.1 × 10 8 Km and $$\textrm{GM}=7\times 10^7 \, \textrm{Km}$$ GM = 7 × 10 7 Km , respectively, Moreover, for $$\textrm{GM}=4.8\times 10^8 \, \textrm{Km}$$ GM = 4.8 × 10 8 Km and $$\textrm{GM}=9.3\times 10^7 \, \textrm{Km}$$ GM = 9.3 × 10 7 Km , the suppression of the entanglement can be observed due to the gravitational effects. Meanwhile, in this case, the gravitational effects also make the distribution of entanglement tighter through investing the entanglement complete monogamy relation. Furthermore, we examine the gravitational effects on the violation of the Svetlichny inequality to study the nonlocality of the system. It is shown that when $$\textrm{GM}=6\times 10^8 \, \textrm{Km}$$ GM = 6 × 10 8 Km and $$\textrm{GM}=7\times 10^7 \, \textrm{Km}$$ GM = 7 × 10 7 Km , the gravitational effects make the Svetlichny parameters always greater than 4, implying that the genuine tripartite nonlocality of the system is always present. However, the gravitational effects also restrain the violation of the Svetlichny to make the regions of the absence of nonlocality increase. The gravitational effects on the monogamy property of nonlocality lies in the change of the effective bound of the maximum bipartite nonlocality of the neutrinos system. Therefore, our investigations may be helpful to understanding of quantumness of the neutrinos system in curved space-time.

DOI
10.1140/epjc/s10052-024-13493-z

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Abstract In this paper, we explore the quantum properties of three-flavor neutrino propagating in a Schwarzschild metric. It is found that the different strength of gravitational effects are obtained by adjusting the magnitude of GM\mathrm GMGM G M arising in the oscillation phase. Using the weak field approximations, we show that the gravitational effects can make the entanglement oscillates over a large rage when GM=5.1×108 Km\textrm{GM}=5.1\times 10^8 \, \textrm{Km}GM=5.1×108Km GM = 5.1 × 10 8 Km and GM=7×107 Km\textrm{GM}=7\times 10^7 \, \textrm{Km}GM=7×107Km GM = 7 × 10 7 Km , respectively, Moreover, for GM=4.8×108 Km\textrm{GM}=4.8\times 10^8 \, \textrm{Km}GM=4.8×108Km GM = 4.8 × 10 8 Km and GM=9.3×107 Km\textrm{GM}=9.3\times 10^7 \, \textrm{Km}GM=9.3×107Km GM = 9.3 × 10 7 Km , the suppression of the entanglement can be observed due to the gravitational effects. Meanwhile, in this case, the gravitational effects also make the distribution of entanglement tighter through investing the entanglement complete monogamy relation. Furthermore, we examine the gravitational effects on the violation of the Svetlichny inequality to study the nonlocality of the system. It is shown that when GM=6×108 Km\textrm{GM}=6\times 10^8 \, \textrm{Km}GM=6×108Km GM = 6 × 10 8 Km and GM=7×107 Km\textrm{GM}=7\times 10^7 \, \textrm{Km}GM=7×107Km GM = 7 × 10 7 Km , the gravitational effects make the Svetlichny parameters always greater than 4, implying that the genuine tripartite nonlocality of the system is always present. However, the gravitational effects also restrain the violation of the Svetlichny to make the regions of the absence of nonlocality increase. The gravitational effects on the monogamy property of nonlocality lies in the change of the effective bound of the maximum bipartite nonlocality of the neutrinos system. Therefore, our investigations may be helpful to understanding of quantumness of the neutrinos system in curved space-time.
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 nonclassicality such as Mermin and Svetlichny inequalities are investigated. Since the extent of neutrino-antineutrino oscillation is governed by the strength of the gravitational field, the behavior of nonclassicality 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.
In this paper, we investigate the quantum coherence for two flavor neutrinos propagating in a Schwarzschild metric. In fact, this issue is explored both qualitatively via calculating the parameter K3{K}_{3}K3​ in Leggett-Garg inequality and also quantitatively by evaluating the l1{l}_{1}l1​-norm, $\mathcal{C}(\ensuremath{\rho})$. Using the weak field approximations, we show that the gravitational effects decrease the maximum value of K3{K}_{3}K3​ for some intervals of energy in such a way that there is no violation, while it leaves the maximum amount of the quantum coherence, $\mathcal{C}(\ensuremath{\rho})$, unchanged.
Quantum phases establish a connection between gravitation and quantum information, offering a novel avenue for exploring the properties of space-time. In this paper, we investigate the quantum correlations (QCs) of neutrinos in the Kerr--Newman space-time for both zero- and nonzero-angular-momentum propagation. The results show that, for zero-angular-momentum propagation, the oscillation periods of the survival probability and QCs progressively decrease with propagation distance in the inward direction. In the outward direction, increasing MMM lengthens the oscillation periods of Pνe→νeP_{ν_e\rightarrowν_e}Pνe​→νe​​, entanglement, and the monogamy of nonlocality, whereas increasing the angular momentum aaa or charge QQQ shortens them. For nonzero-angular-momentum propagation, the metric parameters also generate local profile modulations through additional two-path interference terms, rather than merely rescaling the oscillation period. Furthermore, we find that, despite differences in their ranges of variation, entanglement and coherence exhibit highly consistent oscillatory behavior in both propagation cases. These findings provide a comprehensive understanding of neutrino-based relativistic quantum information.
Abstract The monogamy relation of quantum states has limited the shareability properties of quantum resources in multiparty quantum systems. It plays a vital role in information distribution and transformation over many sites in quantum communications. Here, we focus on the monogamy relations of quantum correlations in the context of three-flavor neutrino oscillations, related to the squared entanglement of formation, the squared of quantum discord and its geometric variant. The monogamy relations in terms of the squared entanglement of formation work for the electron and muon antineutrino oscillations, suggesting that the bipartite entanglement measured by squared entanglement of formation of the three-flavor neutrino system set a limitation to the sum of pairwise squared entanglement of formation. Furthermore, we found that the squared quantum discord is also monogamous in three-flavor neutrino system. As a comparison, we test the monogamy of the quantum discord in neutrino oscillations with the result that the quantum discord is not monogamous. In addition, it is found that the bipartite geometric quantum discord of three-flavor systems is equal to the sum of the pairwise geometric quantum discord, i.e., the monogamy relation for geometric quantum discord is saturated for three-flavor neutrino system. These monogamy relations of quantum correlations provide a way for studying the distribution of quantum resources in neutrino oscillations, which is of significance to explore the further applications of neutrino oscillations in quantum communications.
The flavor oscillations in the neutrino system are known to be related to the multimode entanglement of a single particle state. Neutrino oscillations are shown to encompass not only quantum superposition among different mass eigenstates but also a single-particle multimode entanglement in the flavor basis as they propagate. In the framework of three flavor neutrino oscillations, we demonstrate that the measures of entanglement can be expressed in terms of experimentally accessible appearance and disappearance probabilities. We explicitly show here that the genuine tripartite entanglement measure, i.e., the tangle, vanishes identically for all flavors, signifying that a three flavor neutrino system forms a W-type entangled state. Further, we investigate alternative measures of tripartite entanglement like the partial tangle and the concurrence fill, which capture the total sharing of entanglement beyond pairwise correlations. In terms of bipartite and bipartitioned entanglement measures, we derive the symmetric invariant and the concurrence fill, which quantify the distributed entanglement and are completely expressible in terms of flavor transition probabilities. These entanglement measures display distinct energy dependent patterns across the oscillation window, which can be experimentally accessible in the long baseline experiments like DUNE, providing an alternative quantum information perspective on flavor evolution. We use General Long Baseline Experiment Simulator simulations within the DUNE setup to investigate these tripartite entanglement measures in terms of neutrino energy and the length of the baseline. It is observed that, at the point of maximal mixing, these measures show near maximal entanglement between the muon and the tau flavor modes, establishing entanglement monogamy. Within the DUNE setup, the wide band of energy and expected higher sensitivity to C P violation at the second oscillation maximum provide a unique advantage to explore the quantum correlation effects across a broader energy window. Thus, the flavor coherence and C P -phase dependent interference can influence the quantum entanglement measures among neutrino flavor modes, and thereby, such potential new physics effects can be probed in current or future planned neutrino experiments.
Studying the quantum resources of neutrino oscillations is a topic worth exploring. This review mainly introduces the use of quantum resource theory to characterize the quantum resource characteristics of three-flavor neutrino oscillations, and the specific evolutionary patterns of different entanglement measures in three-flavor neutrino oscillations. In addition, by comparing the cases of different entanglement evolutions, the optimal method of quantifying entanglement in three-flavor neutrino oscillations can be obtained. Moreover, this review also focuses on the quantifying the quantumness of neutrino oscillation observed experimentally by using the l1-norm of coherence. The maximal coherence is observed in the neutrino source from the KamLAND reactor. Furthermore, we examine the violation of the Mermin inequality and Svetlichny inequality to study the nonlocality in three-flavor neutrino oscillations. It is shown that even though the genuine tripartite nonlocal correlation is usually existent, it can disappear within specific time regions. In addition, this review also presents the trade-off relations in the quantum resource theory of three-flavor neutrino oscillations, mainly based on monogamy relations and complete complementarity relations. It is hoped that this review can bring inspiration to the development of this field.