Factorizable maps and traces on the universal free product of matrix\n algebras

2019/03/25 by Magdalena Musat, Musat, Magdalena, Mikael Rørdam +1 · 1 citation
Computer Science · Mathematics · #46L10 #47L90 #81P45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Information and Cryptography

paper · pdf · doi:10.48550/arxiv.1903.10182

openalex publication_date 2019/03/25 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We relate factorizable quantum channels on M_n, for n \≥ 2, via their\nChoi matrix, to certain correlation matrices, which, in turn, are shown to be\nparametrized by traces on the unital free product M_n * M_n. Factorizable\nmaps that admit a finite dimensional ancilla are parametrized by finite\ndimensional traces on M_n * M_n, and factorizable maps that approximately\nfactor through finite dimensional C*-algebras are parametrized by traces in the\nclosure of the finite dimensional ones. The latter set is shown to be equal to\nthe set of hyperlinear traces on M_n * M_n. We finally show that each\nmetrizable Choquet simplex is a face of the simplex of tracial states on M_n *\nM_n.\n

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