Almost All Quantum Channels Are Diagonalizable

Abstract

We prove the statement "The collection of all elements of which have only simple eigenvalues is dense in "for different sets , 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.