发表机构
Faculty of Sciences, Universidad Autónoma del Estado de México; TecNM Tecnológico de Estudios Superiores de Jocotitlán（墨西哥自治州大学理学院; 霍科蒂特兰高等技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文统一了Fisher信息在薛定谔动力学、二分关联与退相干中的角色，揭示了纯态并发度与QFIM优化元素的关系，并利用凸包扩展至混合态，同时区分了经典与量子Fisher信息。
AI 中文摘要
Fisher信息在量子理论中以两种数学上不同的形式出现：一种是在薛定谔动力学的变分重构中作为经典概率泛函，另一种是参数化密度算子的量子Fisher度量。在此，我们考察在不将这两个对象等同的情况下，这些角色能在多大程度上被联系起来。从Hamilton-Jacobi系综作用量出发，我们恢复了产生量子势的Fisher项，并分离出其对动能期望值的贡献。随后，我们分析了二分态的量子Fisher信息矩阵（QFIM）。对于任意纯两量子比特态，归一化局域生成元的QFIM非对角元优化幅度等于并发度，而集体相位生成元则给出F_Q = 4 C^2。通过凸包将优化的纯态量扩展到任意混合两量子比特态，得到与Wootters并发度的精确恒等式。这与直接在混合密度算子上评估QFIM不同：对于Werner态，原始优化的交叉QFIM为2 p^2/(1 + p)，且在可分离区域内保持非零。因此，原始量与凸包量之间的差距，对于该族态，隔离了纠缠未捕捉到的关联几何。最后，在带有which-way标记的双路径干涉仪中，从局域输出统计可获得的优化相位Fisher信息为I_phi^opt = V^2。这些结果将概率梯度能量、二分关联几何、纠缠以及退相干引起的局域相位灵敏度损失置于一个共同的数学框架中，同时保持了经典Fisher信息、QFIM几何、Bell非定域性和全局相位量子化之间的区别。
英文摘要
Fisher information appears in quantum theory in two mathematically distinct settings: as a classical probability functional in variational reconstructions of Schrodinger dynamics and as the quantum Fisher metric of parameterized density operators. Here we examine how far these roles can be connected without identifying the two objects. Starting from a Hamilton-Jacobi ensemble action, we recover the Fisher term that generates the quantum potential and isolate its contribution to the kinetic-energy expectation. We then analyze the quantum Fisher information matrix (QFIM) of bipartite states. For any pure two-qubit state, the optimized magnitude of the off-diagonal QFIM element for normalized local generators equals the concurrence, while a collective phase generator yields FQ = 4 C^2. Extending the optimized pure-state quantity by a convex roof gives an exact identity with Wootters concurrence for arbitrary mixed two-qubit states. This differs from evaluating the QFIM directly on a mixed density operator: for Werner states the raw optimized cross-QFIM is 2 p^2/(1 + p) and remains nonzero inside the separable region. The gap between the raw and convex-roof quantities therefore isolates, for this family, correlation geometry not captured by entanglement. Finally, in a two-path interferometer with a which-way marker, the optimal phase Fisher information available from local output statistics is I_phi^opt = V^2. These results place probability-gradient energy, bipartite correlation geometry, entanglement, and decoherence-induced loss of local phase sensitivity in a common mathematical setting while preserving the distinctions between classical Fisher information, QFIM geometry, Bell nonlocality, and global phase quantization.
