AI 中文总结
研究时空量子态多个记录条件描述能否有单个潜在过程这一一致性问题，结合分支分辨QSOST干涉测量等方法，构造二分量子比特示例，得出相关结果，建立了QSOST与全局过程一致性操作边界并提供测试框架。
AI 中文摘要
确定多个记录条件下的量子描述是否允许单个潜在过程，是时空量子态（QSOSTs）和关系量子描述的核心一致性问题。然而，因果不可知干涉测量仅访问低维QSOST投影，不可避免地留下一些过程自由度未解决。我们将分支分辨QSOST干涉测量与正过程提升和半定凸对偶性相结合来刻画这个胶合问题。我们证明每个正权重QSOST分支都有唯一的最小正提升，并将设置实现性和共同过程可实现性都归结为确定性过程支配。利用此标准，我们构造了一个最小的二分量子比特示例，在确定因果顺序$A\prec B$中有两个记录设置和两个结果：每个设置单独可实现，且两者共享相同的完整无条件QSOST，但没有单个确定性过程能联合实现它们。这种分离具有精确的可见度阈值$\eta =1/\sqrt{2}$，允许一个涉及八个干涉测量正交分量的稀疏见证，并且对于满秩过程仍然存在。这些结果在QSOST一致性和全局过程一致性之间建立了一个操作边界，并为测试多个量子视角是否可以共享一个标准量子过程提供了一个实用框架。
英文摘要
Determining whether observations across spacetime arise from one quantum process is central to causal inference and to consistent observer-relative descriptions. For quantum-state-over-spacetime (QSOST) data, this remains obstructed because causally agnostic interferometry compresses process matrices: every setting can appear physical although its hidden positive completions cannot be glued to a common parent. We formulate this as an inverse positive-lift problem and solve it exactly. Each positive-weight QSOST branch has a unique least positive lift, yielding a data-only common-parent criterion. We prove that settingwise realizability implies common-process realizability for every finite family if and only if the QSOST projection is injective on deterministic processes. Thus any normalized information loss can be exposed as a strict gluing failure. For bipartite qubits we identify a $63$-dimensional hidden fiber and construct definite-order separations, including a minimal two-setting, two-outcome example with exact noise threshold $η=1/\sqrt2$ and a sparse interferometric witness. Under explicit causal-access conditions, we also derive exact delayed fact-inference limits and identify the minimal environment; restoring full access removes only the pre--post gap. These results identify the boundary between spacetime tomography and global process composition, turning hidden process incompatibility into an experimentally testable phenomenon.
