Almost All Quantum Channels Are Diagonalizable

Abstract

We prove the statement “The collection of all elements of[Formula: see text] which have only simple eigenvalues is dense in[Formula: see text]” for different sets [Formula: see text], including: all quantum channels, the unital channels, the positive trace-preserving maps, all Lindbladians (gksl-generators), and all time-dependent Markovian channels. Therefore any element from each of these sets can always be approximated by diagonalizable elements of the same set to arbitrary precision.