2024/10/17 by Kyung Hoon Han, Seung-Hyeok Kye, Han, Kyung Hoon +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2410.13120
openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We look for all linear isomorphisms from the mapping spaces onto the tensor products of matrices which send k-superpositive maps onto unnormalized bi-partite states of Schmidt numbers less than or equal to k. They also send k-positive maps onto k-block-positive matrices. We also look for all the bilinear pairings between the mapping spaces and tensor products of matrices which retain the usual duality between k-positivity and Schmidt numbers ≤ k. They also retain the duality between k-superpositivity and k-block-positivity.