AI 中文总结
该研究针对预/后选择量子动力学，采用gEDMD方法提取生成器，揭示两层时间箭头，在晶格干涉仪中观测到量子柴郡猫结构，消除N量子比特重叠障碍。
AI 中文摘要
基于过去和未来的条件设定赋予了因果观察者无法获得的中间时间性质，这些时间对称的设定遵循精确的对称性定理且可从轨迹中测量。我们采用双态生成器扩展动态模式分解（gEDMD）：由于弱值精确满足 $dA_w/dt=i\langle[H,A]\rangle_w$，带精确导数基线的生成器提取可直接应用于弱值。首先，对预/后选择系综的反射对合将每个窗口拟合的摩擦唯一拆分为 $\gamma_{fwd}=\gamma_A+\gamma_S$：关于中点反对称的 $\gamma_A$ 携带模式的边界条件物理，对称的 $\gamma_S$ 来自差分格式；两者均由同一数据通过 $(\gamma_{fwd}\pm\gamma_{bwd})/2$ 得到。在固定推理分辨率下，时间箭头有两层：相干模式箭头在中点反转，涨落层箭头不反转，且在所有尺寸和类别中 $\gamma_S$ 主导 $\gamma_A$；程度差异体现为：此处 $\gamma_S$ 是模式层的34倍，且借助精确导数两层均反转：免疫性属于推理而非系综。其次，在仅以端口为条件的晶格干涉仪中，量子柴郡猫结构自然出现：粒子和偏振遵循各自的连续性方程，偏振携带臂中的局域场使该相位单独旋转，强度恰好为场强的两倍，作为刚性虚位移进入生成器，而粒子的弱密度在机器精度下保持不变。我们从 $2^8$ 到 $2^{20}$ 维验证样本级恒等式和两层结构：跨五个类别 $|\gamma_A|/\gamma_S$ 为0.09至0.27；自平均特性使其对共享边界调制的类别不敏感，消除了N量子比特的 $2^{-N/2}$ 重叠障碍。
英文摘要
Conditioning on both past and future assigns intermediate-time properties a causal observer does not; these time-symmetric assignments obey exact symmetry theorems and are measurable from trajectories. We use two-state generator extended dynamic mode decomposition (gEDMD): because weak values obey $dA_w/dt=i\langle[H,A]\rangle_w$ exactly, generator extraction, with an exact-derivative baseline, applies unchanged to them. First, a reflection involution on the pre-/post-selected ensemble splits every window-fitted friction uniquely as $γ_{fwd}=γ_A+γ_S$: $γ_A$, antisymmetric about the midpoint, carries the modes' boundary-condition physics; $γ_S$, symmetric, comes from the differencing scheme; both follow from the same data as $(γ_{fwd}\pmγ_{bwd})/2$. At a fixed inference resolution the arrow of time has two layers: the coherent-mode arrow reverses at the midpoint, the fluctuation-level one does not, $γ_S$ dominating $γ_A$ at every size and class. The difference is one of degree: $γ_S$ is 34 times larger there than at the mode layer, and with the exact derivative both layers reverse: immunity belongs to the inference, not the ensemble. Second, in a lattice interferometer conditioned only at its ports, the quantum Cheshire-cat structure emerges unimposed: particle and polarization obey separate continuity equations, and a local field in the polarization-carrying arm rotates that phase alone, at exactly twice the field strength, entering the generator as a rigid imaginary shift, while the particle's weak density stays invariant to machine precision. We verify the sample-level identity and the two layers from $2^8$ to $2^{20}$ dimensions: $|γ_A|/γ_S=0.09$ to $0.27$ across five classes; self-averaging makes it insensitive to class among those sharing a boundary modulation, removing the $2^{-N/2}$ overlap obstruction for $N$ qubits.
Comments21 pages, 11 figures, 5 tables
