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The European Physical Journal C

Monogamy properties of quantum correlations in neutrino oscillations

Guang-Jie Wang, Yuwen Li, Lijuan Li, Xue‐Ke Song, Dong Wang

Published Sep 10, 2023• 15 citations
Publisher

Abstract

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.

DOI
10.1140/epjc/s10052-023-11979-w

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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.
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.
In this paper, we obtain the pairwise quantum discord for a three-qubit W-class state, and investigate the monogamy property of quantum discord by two different ways (relative entropy-based distance and geometric square-norm distance). Through numerical calculations, we find that a party cannot have maximal quantum correlations with the other two parties simultaneously. For the given state, the quantum correlation between particles 1 and 3 induces limitation on the quantum correlation between them and particle 2. Moreover, the result also shows that the geometric quantum discord of the given W-class state obeys the monogamy property while the entropy quantum discord violates.
The distribution of quantum correlations in multipartite systems plays a significant role in several aspects of quantum information theory. While it is well known that these quantum correlations cannot be freely distributed, the way that they are shared in a multipartite system is an open problem even for a small set of qubits. Based on monogamylike relations between entanglement and discord for nnn-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.
It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.
NNumerous neutrino experiments have confirmed the phenomenon of neutrino oscillation, providing direct evidence of the quantum mechanical nature of neutrinos. In this work, we investigate the entanglement properties of neutrino flavor states within the framework of three-flavor neutrino oscillation using two major entanglement measures: entanglement of formation (EOF) and concurrence, utilizing the DUNE experimental setup. Our findings indicate that the maximally entangled state appears between ν μ and ν τ whereas, ν e behaves as a nearly separable state. To further explore the nature of bipartite entanglement, we introduce the concept of the monogamy of entanglement, which allows us to investigate the distinction between genuine three-flavor entanglement and bipartite entanglement. Our analysis confirms that the three-flavor neutrino system forms a bipartite entanglement structure, adhering to the Coffman-Kundu-Wootters (CKW) inequality. Additionally, we implement a minimization procedure to find the best-fit values of the oscillation parameters that correspond to the concurrence minima at the two specific energy points where the concurrence reaches its lowest values. Using these best-fit values, we probe three fundamental unknowns in neutrino oscillation: CP violation sensitivity, neutrino mass hierarchy, and the octant issue of θ 23 , across two distinct energy points. Our results manifest that while the best-fit values obtained through concurrence minimization show slightly reduced sensitivity to CP violation compared to current best-fit values, they exhibit greater sensitivity to the mass hierarchy. Furthermore, the study reveals a maximal mixing angle for the atmospheric sector.
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.