中微子振荡中量子资源理论的权衡关系
Trade-off relations of quantum resource theory in neutrino oscillations
摘要：
通过对Leggett-Garg不等式经典边界的突破，验证了中微子振荡（NOs）在长距离传播过程中的量子性。利用量子资源理论（QRT）研究了实验观测到的NO的量子性测度。本文基于Bell型违反、一阶相干性和内禀并发性以及相干性的相对熵，重点研究了三味NO中QRT的权衡关系。对于电子和μ子的反中微子振荡，得到了该三味中微子系统中两两味态的Bell-CHSH不等式所服从的解析折衷关系，三个两两味态的CHSH检验的最大违反之和小于或等于12.此外，NO中的一阶相干性和内禀纠缠度之间存在一个等式关系，表明在中微子传播过程中，有多少量子资源在一阶相干性和内禀纠缠度之间流动.此外，还发现三味态的三重相干等于或大于约化二分味态相干之和。QRT的折衷关系提供了一种研究量子资源在NO中如何转换和分配的方法，这可能会启发未来利用中微子进行量子信息处理的应用。
英文摘要：
The violation of the classical bounds imposed by Leggett-Garg inequalities has tested the quantumness of neutrino oscillations (NOs) over a long distance during the propagation. The measure of quantumness in experimentally observed NOs is studied via quantum resource theory (QRT). Here, we focus on the trade-off relations of QRT in the three-flavor NOs, based on Bell-type violations, first-order coherence and intrinsic concurrence, and the relative entropy of coherence. For the electron and muon antineutrino oscillations, the analytical trade-off relations obeyed by the Bell-CHSH inequality of pairwise flavor states in this three-flavor neutrino system are obtained; the sum of the maximal violation of the CHSH tests for three pairwise flavor states is less than or equal to 12. Moreover, there exists an equality relation concerning first-order coherence and intrinsic concurrence in NOs, showing how much quantum resources flow between first-order coherence and intrinsic concurrence during the neutrino propagation. In addition, it is found that the tripartite coherence of three-flavor system is equal to or larger than the sum of the coherence of reduced bipartite flavor states. The trade-off relations of QRT provide a method for studying how the quantum resources convert and distribute in NOs, which might inspire the future applications in quantum information processing using neutrinos.
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