Commuting Kraus operators are normal

Abstract

Let $\{V_1,\dots ,V_n\}$ be a set of mutually commuting matrices. We show that if $V_1^{\ast }{V}_1+\cdots +V_n^{\ast }{V}_n=\mathrm{Id}$ then the matrices are normal and, in particular, simultaneously diagonalizable.

arXiv comment6 pages