Disentangling tensor product structures

2025/06/26 by Antoine Soulas, Soulas, Antoine · 2 citations
Computer Science · #Coding theory and cryptography #Constructive #FOS: Physical sciences #Hilbert space #Mathematical Physics (math-ph) #Product (mathematics) #Quantum Physics (quant-ph) #Quantum entanglement #Space (punctuation) #Tensor (intrinsic definition) #Tensor product #Tensor product of Hilbert spaces

paper · pdf · doi:10.48550/arxiv.2506.21173

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/08/05

Abstract

As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state, there exists a tensor product structure in which no entanglement is generated. We give a concrete, constructive example of disentangling tensor product structure in the case of a C-NOT gate evolution between two qbits, before showing that this cannot be achieved for most time-evolving quantum states.

Citations

• On the emergence of preferred structures in quantum theory
• What makes you an observer?
• Quantum mereology and subsystems from the spectrum
• To be or not to be, but where?
• A Search for Classical Subsystems in Quantum Worlds
• Does the Hamiltonian determine the tensor product structure and the 3d space?
• The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism
• Reality as a Vector in Hilbert Space
• Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal
• Space from Hilbert space: Recovering geometry from bulk entanglement
• Consciousness as a state of matter
• Nothing happens in the Universe of the Everett Interpretation
• Most tensor problems are NP-hard
• Most Tensor Problems Are NP-Hard
• On the relative quantum entanglement with respect to tensor product structure

Cited by

• On the emergence of preferred structures in quantum theory
• Mereological Quantum Phase Transitions

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