2024/03/26 by Manimugdha Saikia, Saikia, Manimugdha
Mathematics · #15-02 #53D50 #81R30 #81S10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2403.17435
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We associate quantum states with subsets of a product of two compact connected Kähler manifolds M1 and M2. To associate the quantum state with the subset, we use the map that restricts holomorphic sections of the quantum line bundle over the product of the two Kähler manifolds to the subset. We present a description of the kernel of this restriction map when the subset is a finite union of products. This in turn shows that the quantum states associated with the finite union of products are separable. Finally, for every pure state and certain mixed state, we construct subsets of M1× M2 such that the states associated with these subsets are the original states, to begin with.