Exposedness of elementary positive maps between matrix algebras

2023/01/13 by Seung-Hyeok Kye, Kye, Seung-Hyeok · 1 citation
Computer Science · Mathematics · #15A30 #46L05 #46L07 #81P15 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2301.05788

openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The positive linear maps \ad_s which send matrices x to s^*xs play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear Multilinear Alg. 61 (2013), 970--975] that the map \ad_s generates an exposed ray of the convex cone of all positive linear maps. In this note, we provide two alternative proofs, using Choi matrices and Woronowicz's method, respectively.

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