三味中微子振荡的量子资源特性研究

王光杰; 宋学科; 叶柳; 王栋

doi:10.7498/aps.74.20250029

摘要

中微子振荡是一个有趣的物理现象, 其量子性能够在宏观距离的振荡上得以保持并被检测到. 中微子振荡的量子资源特性是一个值得探索的主题, 这种在粒子物理学和量子信息学之间建立起的联系, 对于研究基本粒子的基本性质以及探索将中微子作为一种资源应用于量子信息处理的可能性而言, 都有着重要意义. 因此, 中微子物理学与量子信息理论的交叉研究受到了越来越多的关注. 这篇综述主要介绍利用量子资源理论来表征三味中微子振荡的量子资源特性, 包括量子纠缠、量子相干、量子非局域性和熵不确定度等. 除此之外, 还介绍了三味中微子振荡中的量子资源理论的权衡关系, 主要基于单配性关系和完全互补性关系, 这些权衡关系可以帮助我们有效理解量子资源如何在中微子振荡中转化和分配. 中微子振荡的量子信息理论研究仍处于不断发展中, 期望本综述能为该领域的发展带来启示.

关键词:

Abstract

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.

Keywords:

作者及机构信息

安徽大学物理与光电工程学院, 合肥　230601

通信作者: 宋学科, songxk@ahu.edu.cn

基金项目: 国家自然科学基金(批准号: 62471001, 12475009, 12075001, 12175001, 12004006)、安徽省自然科学基金(批准号: 2022b13020004, 2008085QA43)和安徽省高校科研计划(批准号: 2024AH050068, 2024AH040008)资助的课题.

Authors and contacts

School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, China

Corresponding author: SONG Xueke, songxk@ahu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62471001, 12475009, 12075001, 12175001, 12004006), the Natural Science Foundation of Anhui Province, China (Grant Nos. 2022b13020004, 2008085QA43), and the Scientific Research Project of Universities in Anhui Province, China (Grant Nos. 2024AH050068, 2024AH040008).

文章全文

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施引文献

图 1 四种不同种类的纠缠度量, 包括广义的几何测量(GGM)、three-π纠缠、多体共生纠缠(GMC)、concurrence fill, 在三味电子中微子振荡系统和三味μ子中微子振荡系统中的时间演化^[51]　(a) 三味电子中微子系统中不同多体纠缠测度的演化图像; (b) 三味μ子中微子系统中不同多体纠缠测度的演化图像

Fig. 1. Four kinds of multipartite entanglement measures, including generalized geometric measure (GGM), three-π, genuinely multipartite concurrence (GMC), and the concurrence fill for three flavors electron neutrino oscillation system and three flavors muon neutrino oscillations^[51]: (a) Dynamic of different multipartite entanglement measures in three flavor electron neutrino system; (b) dynamic of different multipartite entanglement measures in three flavor muon neutrino system.

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图 2 $K_3$对于三个不同实验设置的能量变化^[78]　(a), (b) DUNE; (c), (d) NOνA; (e), (f) T2K. 其中CP破坏相位δ取不同的值, 时间可以用长度(基线)来确定, DUNE, NOνA和T2K的长度分别为1300, 810和295 km. (a), (c), (e)对应于初始中微子态; (b), (d), (f)对应于初始反中微子态

Fig. 2. The Variations in K₃ as a function of the energy for three experimental setups for different values of the CP-violating phase δ^[78]: (a), (b) DUNE; (c), (d) NOνA; (e), (f) T2K. The time can be identified with the length (baseline) which is 1300, 810 and 295 km for DUNE, NOνA and T2K, respectively. The panels (a), (c), (e) correspond to the initial neutrino state, and panels (b), (d), (f) correspond to the initial antineutrino state.

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图 3 三味电子中微子振荡情况下理论与实验中的相干^[40]　 (a)来自于大亚湾三个地下实验所获取的实验数据下的相干, 分别由EH1, EH2, EH3对应的误差棒描述; (b) KamLAND合作实验的中微子振荡相干. 图(a)插图分别展示了相干对于中微子生存概率以及比率ξ的导数. 图中红线是理论上的相干, 红色带状区域是理论拟合预测值周围的3σ置信区间的相干. 误差棒所展示的相干在短距离情况下与理论3σ范围内一致

Fig. 3. Coherence in theory and experiment for three-flavor electron neutrino oscillations^[40]: (a) Coherence based on the experimental data obtained from the Daya Bay collaboration in three underground experimental halls, which is described by the error bars corresponding to EH1, EH2 and EH3 respectively; (b) coherence of neutrino oscillations under the T2K collaboration. The insets in panel (a) show the derivatives of coherence with respect to the neutrino survival probability and the ratio ξ. The red line in the picture shows the coherence in theory, and the red band indicates the coherence within the 3σ confidence interval around the theoretically fitted prediction. The coherence indicated by the error bars is consistent with the theoretical 3σ range in the short-distance case

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图 4 三味μ子中微子振荡情况下理论与实验中的相干^[40]. 图中红线是理论上的相干, 红色带状区域是理论拟合预测值周围的3σ置信区间的相干, 黑色方块展示的MINOS合作实验的中微子振荡相干, 蓝色圆圈是T2K实验中微子振荡相干. 误差棒所展示的相干在短距离情况下与理论3σ范围内一致

Fig. 4. The coherence in theory and experiment for three-flavor μ neutrino oscillations^[40]. The red line shows the coherence in theory, and the red band indicates the coherence within the 3σ confidence interval around the theoretically fitted prediction. The black squares show the coherence of neutrino oscillations in the MINOS collaboration, while the blue circles show the coherence of neutrino oscillations in the T2K collaboration. The coherence indicated by the error bars is consistent with the theoretical 3σ range in the short-distance case.

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图 5 三味中微子振荡情况下参数$M_3$的变化^[50]　(a)初始电子中微子; (b)初始μ子中微子; (c)初始τ子中微子. 黑色虚线对应于$M_3$的经典界限

Fig. 5. Variation of the parameter $M_3$ for three-flavor neutrino oscillations^[50]: (a) Initial electron neutrino oscillation; (b) initial μ neutrino oscillation; (c) initial τ neutrino oscillation. The black dotted line corresponds to the classical bound of $M_3$.

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图 6 三味中微子振荡情况下参数$S_3$的变化^[50]　(a)初始电子中微子; (b)初始μ子中微子; (c)初始τ子中微子. 黑色虚线对应于$S_3$的经典界限

Fig. 6. Variation of the parameter $S_3$ for three-flavor neutrino oscillations^[50]: (a) Initial electron neutrino oscillation; (b) initial μ neutrino oscillation; (c) initial τ neutrino oscillation. The black dotted line corresponds to the classical bound of $S_3$.

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图 7 总的熵不确定度在三味电子和μ子中微子振荡中的演化^[65]　(a)总的熵不确定度在电子中微子振荡中的演化, 其中EH1, EH2和EH3是大亚湾合作项目针对三个不同实验提供的数据; (b)总的熵不确定度在电子中微子振荡中的演化. 橄榄线表示总的熵不确定度的理论值, 红线是(62)式中的右式, 对应于总的熵不确定关系的下届, 黑色方块代表MINOS+合作项目的实验数据

Fig. 7. The evolution of the total entropic uncertainty in three flavor electron and μ neutrino oscillations^[65]: (a) The evolution of the total entropic uncertainty in electron neutrino oscillation, where EH1, EH2 and EH3 are the data addressed from Daya Bay collaboration for three different experimental; (b) the evolution of the total entropic uncertainty in muon neutrino oscillation. The olive line represents the theoretical value of the total entropic uncertainty, and the red line corresponds to the lower bound of the total entropic uncertainty relation. The black squares stand for the experiment data from MINOS+ collaboration.

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图 8 三味电子中微子振荡情况下的单配性关系验证^[66]　(a)电子中微子振荡中的剩余形成纠缠的平方; (b)剩余失谐的平方与剩余失谐的对比; (c)电子中微子振荡中几何失谐的单配性验证, 可以观察到单配性关系$D_{\mathrm{G}}(\rho^{\mathrm{e}}_{AB})+D_G{\mathrm{}}(\rho^{\mathrm{e}}_{{AC}})=D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{A}\mid {BC}})$在电子中微子振荡中始终保持

Fig. 8. Tests of the monogamy relation for three-flavor electron neutrino oscillations^[66]: (a) The residual squared entanglement of formation in the electron neutrino oscillations; (b) the residual squared of quantum discord in comparison to the residual quantum discord; (c) the monogamy of the geometric measure of quantum discord in electron neutrino oscillations. One can see that the monogamy relation $D_{\mathrm{G}}(\rho^{\mathrm{e}}_{AB})+D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{{AC}}})=D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{A}\mid {BC}})$ holds in electron tineutrino oscillations.

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图 9 三味μ子中微子振荡情况下的单配性关系验证^[66]　(a) μ子中微子振荡中的剩余形成纠缠的平方; (b)剩余失谐的平方与剩余失谐的对比; (c) μ子中微子振荡中几何失谐的单配性验证, 可以观察到单配性关系$D_{\mathrm{G}}(\rho^{\mathrm{e}}_{AB})+D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{{AC}}})=D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{A}\mid {BC}})$在μ子中微子振荡中始终保持

Fig. 9. Tests of the monogamy relation for three-flavor muon neutrino oscillations^[66]: (a) The residual squared entanglement of formation in the μ neutrino oscillations; (b) the residual squared of quantum discord in comparison to the residual quantum discord; (c) the monogamy of the geometric measure of quantum discord in μ neutrino oscillations. One can see that the monogamy relation $D_{\mathrm{G}}(\rho^{\mathrm{e}}_{AB})+D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{{AC}}})=D_{\mathrm{G}}(\rho^{\mathrm{e}}_{{A}\mid {BC}})$ holds in muon tineutrino oscillations.

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图 10 (55)式描述的完全互补性关系中的关联度量在三味中微子振荡中的演化^[58]　(a)电子中微子振荡中的完全互补性关系中的关联演化; (b) μ子中微子振荡中的完全互补性关系中的关联演化

Fig. 10. Evolution of the correlation measures in the complete complementarity relations described by Eq. (55) in three-flavor neutrino oscillations^[58]: (a) Evolution of the correlation measures in the complete complementarity relations for electron neutrino oscillations; (b) evolution of the correlation measures in the complete complementarity relations for μ neutrino oscillations.

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图 11 (53)式描述的完全互补性关系中的相关项在三味电子中微子振荡中的演化^[58]　(a)子系统${\mathrm{e}}{\text{μ}}$中的完全互补性关系; (b)子系统${\mathrm{e}}{\text{τ}}$中的完全互补性关系; (c)子系统${\text{μ}}{\text{τ}}$中的完全互补性关系

Fig. 11. The complete complementarity relation terms for three-flavor electron neutrino oscillations^[58]: (a) The complete complementarity relation terms for ${\mathrm{e}}{\text{μ}}$ subsystem; (b) the complete complementarity relation terms for ${\mathrm{e}}{\text{τ}}$ subsystem; (c) the complete complementarity relation terms for ${\text{μ}}{\text{τ}}$ subsystem.

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图 12 (53)式描述的完全互补性关系中的相关项在三味μ子中微子振荡中的演化^[58]　(a)子系统${\mathrm{e}}{\text{μ}}$中的完全互补性关系; (b)子系统${\mathrm{e}}{\text{τ}}$中的完全互补性关系; (c)子系统${\text{μ}}{\text{τ}}$中的完全互补性关系

Fig. 12. The complete complementarity relation terms for three-flavor muon neutrino oscillations^[58]: (a) The complete complementarity relation terms for ${\text{e}}{\text{μ}}$ subsystem; (b) the complete complementarity relation terms for ${\mathrm{e}}{\text{τ}}$ subsystem; (c) the complete complementarity relation terms for ${\text{μ}}{\text{τ}}$ subsystem.

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三味中微子振荡的量子资源特性研究