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Frederik vom Ende (Mar 29 2024).

Abstract: We prove the statement “The collection of all elements of $\mathcal S$ which have only simple eigenvalues is dense in $\mathcal S$” for different sets $\mathcal S$, 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.

Arxiv: https://arxiv.org/abs/2403.19643