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International Journal of Quantum Information

Complete complementarity relations for quantum correlations in neutrino oscillations with CP violation

Massimo Blasone A, Silvio De Siena, Cristina Matrella

Published Jan 20, 2024• 3 citations
Publisher

Abstract

We characterize quantum correlations encoded in a three-flavor oscillating neutrino system by taking into account CP violation. By means of the complete complementarity relations (CCR), we study the trade-off of predictability, local coherence and nonlocal correlations by using relevant parameters given by neutrino oscillation experiments. Although the CCR describe very well the contributions associated to bipartite correlations, we explore the possible presence of genuine tripartite correlations, by exploiting polygamy relations. We also provide some observations about the nonlocal advantage of quantum coherence, a mazy quantum correlation characterizing the most valuable, nonlocal, portion of quantum coherence in a multi-partite system.

DOI
10.1142/s0219749924500035

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We investigate wave--particle--entanglement complementarity in three-flavor neutrino oscillations within a quantum information--theoretic framework. Treating neutrino flavor evolution as an open quantum system and explicitly accounting for detector--propagation correlations, we extend the conventional wave--particle duality relation to a triality relation involving predictability, visibility, and entanglement. Using reduced density matrices and I-concurrence as a quantitative measure of entanglement, we demonstrate that the total information content of the system satisfies the relation P2+V2+E2=1\mathcal{P}^2 + \mathcal{V}^2 + \mathcal{E}^2 = 1P2+V2+E2=1. While predictability and visibility exhibit the expected complementary behavior, we show that entanglement encodes additional wave-like information that is not captured by visibility alone. We apply our formalism to realistic long-baseline neutrino experiments, namely \textsf{DUNE} and \textsf{T2K}, and find that at the first oscillation maximum, a simultaneous characterization of the particle-like and wave-like nature of neutrinos becomes possible through the combined measurement of predictability and entanglement. Our results provide a unified operational interpretation of neutrino oscillations and highlight the role of quantum correlations in extending wave--particle duality to multipartite systems.
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.