When Quantum States over Spacetime Have No Common Process

• URL: http://arxiv.org/abs/2607.25899v2
• Date: Wed, 29 Jul 2026 15:55:24 GMT
• Title: When Quantum States over Spacetime Have No Common Process
• Abstract summary: We prove that settingwise realizability implies common-process realizability for every finite family.<n>For bipartite qubits we identify a $63$-dimensional hidden fiber and construct definite-order separations.<n>These results identify the boundary between spacetime tomography and global process composition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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