2023/03/26 by Rafael D. Sorkin, Sorkin, Rafael D.
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2303.14596
openalex publication_date 2023/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a vector-space ~V~ which is the tensor product of vector-spaces A and B, we reconstruct A and B from the family of simple tensors a⊗b within V. In an application to quantum mechanics, one would be reconstructing the component subsystems of a composite system from its unentangled pure states. Our constructions can be viewed as instances of the category-theoretic concepts of functor and natural isomorphism, and we use this to bring out the intuition behind these concepts, and also to critique them. Also presented are some suggestions for further work, including a hoped-for application to entanglement entropy in quantum field theory.