Entanglement and products

2021/04/21 by Tatyana Barron, Barron, Tatyana, Noah Wheatley +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2104.10597

openalex publication_date 2021/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a sequence of quantum states, ρ_N, associated with a submanifold Λ of product of two integral compact Kähler manifolds. We show that, when Λ is a product submanifold, then, in the semiclassical limit, these states are not entangled. We discuss whether geometry of Λ (specifically Λ being a product submanifold) has any relationship with entanglement properties of ρ_N.

Related

• Product-State Manifolds for M Quantum Systems with N Levels using the Fano form and the Induced Euclidean Metric
• Geometry and Product States
• Semiclassical asymptotics and entropy
• Restrictions of holomorphic sections to products
• Further de-Entangling Entanglement