Quantum Entanglement as a Cohomological Obstruction

• URL: http://arxiv.org/abs/2511.04326v1
• Date: Thu, 06 Nov 2025 12:55:28 GMT
• Title: Quantum Entanglement as a Cohomological Obstruction
• Authors: Kazuki Ikeda,
• Abstract summary: We recast quantum entanglement as a cohomological obstruction to reconstruct a global quantum state from locally compatible information.<n>We introduce a Quantum Entment Index (QEI) as an index-theoretic invariant of entangled states and explain its behavior.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses. Sheafification erases the global-from-local signature while leaving within-patch multipartite structure, captured by local entanglement groups introduced here. For smooth parameter families, the obstruction admits a differential-geometric representative obtained by pairing an appropriate witness field with the curvature of a natural unitary connection on the associated bundle of amplitudes. We also introduce a Quantum Entanglement Index (QEI) as an index-theoretic invariant of entangled states and explain its behavior. Finally, we outline a theoretical physics approach to probe these ideas in quantum many-body systems and suggest a possible entanglement-induced correction as an experimental target.

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