arXiv:2403.19643quant-ph
Almost All Quantum Channels Are Diagonalizable
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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.
A bridge too far atm? Here's an (intermediate) interpolate: https://arxiv.org/abs/2403.19643v3 "CUBITT [10]" E: TIGR- EAB reminds gen++ to choose their parents wisely The correct and elegant thing, I felt, was to be of gentle birth but to have no money.
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