Commuting Kraus operators are normal

2023/08/10 by Martin Fraas, Fraas, Martin
Computer Science · Mathematics · #Advanced Topics in Algebra #Combinatorics #Computer science #Diagonalizable matrix #Eigenvalues and eigenvectors #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Mathematics #Matrix Theory and Algorithms #Normal matrix #Physics #Pure mathematics #Quantum mechanics #Rings and Algebras (math.RA) #Set (abstract data type) #Symmetric matrix

paper · pdf · doi:10.48550/arxiv.2308.05450

openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Let \V₁, …, V_n \ be a set of mutually commuting matrices. We show that if V₁^* V₁ + ⋯ +V_n^* V_n = \rm Id then the matrices are normal and, in particular, simultaneously diagonalizable.

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• Almost commuting matrices with respect to normalized Hilbert-Schmidt norm
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