Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914117367889920 |
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| author | Ende, Frederik vom Chruściński, Dariusz Kimura, Gen Muratore-Ginanneschi, Paolo |
| author_facet | Ende, Frederik vom Chruściński, Dariusz Kimura, Gen Muratore-Ginanneschi, Paolo |
| contents | We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps Ende, Frederik vom Chruściński, Dariusz Kimura, Gen Muratore-Ginanneschi, Paolo Rings and Algebras Mathematical Physics Dynamical Systems Quantum Physics We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic. |
| title | Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps |
| topic | Rings and Algebras Mathematical Physics Dynamical Systems Quantum Physics |
| url | https://arxiv.org/abs/2506.02145 |