发表机构
Dipartimento di Fisica e Chimica “Emilio Segrè”, Università degli Studi di Palermo; DSIMB, Inserm, BIGR U1134, Université Paris Cité & Université de La Réunion; Life Actuarial Department, Taiwan Insurance Institute（巴勒莫大学物理与化学系; 巴黎西岱大学 & 留尼汪大学; 台湾保险研究所生命精算部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示量子薛定谔桥构造的正性假设在预选-后选两态振幅的节点轨迹上失效，阐明弱动量的扩散表示存在节点阻碍，并给出双缝实验中可检验的特征信号。
AI 中文摘要
量子薛定谔桥构造在端点数据的正性假设下确立了条件过程的存在性，且有三类独立的构造采用了这一假设。我们证明，当条件对象为构型空间上预选-后选对的两态振幅$\phi^*\psi$时，该假设会在一个确定的轨迹上失效，且这种失效可在记录数据中得到检验。每当$\phi^*\psi$存在一个k阶运动零点，且有概率流穿过该零点时，任何具有恒定扩散系数的扩散过程都无法既承载条件密度又避开节点曲线：它所需的流速度会随到该曲线距离的2k次反比增长，且在一侧指向该曲线，使曲线处于有限标度距离处，因此会被到达而非仅仅被趋近。将弱动量等同于桥漂移的做法本身也不成立：对于位置后选的自由粒子，流速度恰好等于指向目标的桥漂移的负值。正Doob h变换（正杜布h变换）以及建立在其上的伯恩斯坦条件作用在$\phi^*\psi$无节点的所有位置都存在，而在节点曲线上失效。在节点曲线处，弱动量的渗透部分随到零点的距离反比发散，且穿过零点时符号发生改变，系数由k决定，而流部分保持有界；这种有界性依赖于实包络类的带符号分解，且会在任何仅基于流速度构建的图像中掩盖该阻碍。测得的条纹可见度确定了一个单一长度，如果对比度受离轴零点限制，这会在双缝轨迹实验重构的流通道中引入一个量级为$10^{-3}$的洛伦兹型分布，而如果对比度由非相干性限制，则不会出现该分布。本研究的结果是一维的，覆盖了双缝几何的可分离横向场，而非一般的二维涡旋。
英文摘要
Quantum Schrödinger bridge constructions establish the existence of a conditioned process under a positivity hypothesis on the endpoint data, and three independent ones adopt it. We show that hypothesis fails on a definite locus once the conditioned object is the two-state amplitude $ϕ^*ψ$ of a pre- and post-selected pair on configuration space, and that the failure is testable on recorded data. Whenever $ϕ^*ψ$ has a moving zero of order $k$ across which probability flows, no diffusion of constant diffusion coefficient can both carry the conditioned density and avoid the nodal curve: the current velocity it would need grows as the inverse $2k$-th power of the distance to that curve and points toward it on one side, placing the curve at finite scale distance, so it is reached and not merely approached. Identifying the weak momentum with a bridge drift fails independently: for a free particle post-selected in position the current velocity is exactly minus the drift of the bridge to the target. The positive Doob $h$-transform and the Bernstein conditioning built on it exist wherever $ϕ^*ψ$ is nodeless and fail on the nodal curve. There the osmotic part of the weak momentum diverges as the inverse distance to the zero and changes sign across it with a coefficient set by $k$, while the current part stays bounded; that boundedness rests on the signed factorization of the real-envelope class and hides the obstruction from any picture built on the current velocity alone. A measured fringe visibility fixes a single length, which puts a Lorentzian of order $10^{-3}$ into the current channel reconstructed in the two-slit trajectory experiment if the contrast is limited by an off-axis zero, and nothing there if by incoherence. The results are one-dimensional, covering the separable transverse field of a two-slit geometry, not general two-dimensional vortices.
Comments29 pages, 7 figures, 3 tables. Verification code: doi:10.5281/zenodo.21846293
