Indecomposable exposed positive bi-linear maps between two by two matrices

2017/09/20 by Seung-Hyeok Kye, Kye, Seung-Hyeok
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Quantum Information and Cryptography

paper · pdf · doi:10.48550/arxiv.1709.06705

openalex publication_date 2017/09/20 · openalex created_date 2017/10/06 · openalex updated_date 2026/07/28

Abstract

Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between 2× 2 matrices which generate extreme rays in the cone of all positive bi-linear maps. In fact, they are exposed, and so detect entanglement of positive partial transpose whose volume is nonzero.

Citations

• Separable States with Unique Decompositions
• Completely positive linear maps on complex matrices

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