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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.19643 |
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| _version_ | 1866917766887374848 |
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| author | Ende, Frederik vom |
| author_facet | Ende, Frederik vom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost All Quantum Channels Are Diagonalizable Ende, Frederik vom Quantum Physics 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. |
| title | Almost All Quantum Channels Are Diagonalizable |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.19643 |