Quasi-stationary normal states for quantum Markov semigroups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909729562820608 |
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| author | Dhahri, Ameur Fagnola, Franco Girotti, Federico Yoo, Hyun Jae |
| author_facet | Dhahri, Ameur Fagnola, Franco Girotti, Federico Yoo, Hyun Jae |
| contents | We introduce the notion of Quasi-Stationary State (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation of QSSs using the theory of direct and indirect quantum measurements. Moreover, we prove that there is a connection between QSSs and spectral properties of the quantum Markov semigroup. Finally, we discuss some examples which, despite their simplicity, already show interesting features. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06396 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-stationary normal states for quantum Markov semigroups Dhahri, Ameur Fagnola, Franco Girotti, Federico Yoo, Hyun Jae Quantum Physics Dynamical Systems Operator Algebras Probability 46L53, 81S22, 46L57 We introduce the notion of Quasi-Stationary State (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation of QSSs using the theory of direct and indirect quantum measurements. Moreover, we prove that there is a connection between QSSs and spectral properties of the quantum Markov semigroup. Finally, we discuss some examples which, despite their simplicity, already show interesting features. |
| title | Quasi-stationary normal states for quantum Markov semigroups |
| topic | Quantum Physics Dynamical Systems Operator Algebras Probability 46L53, 81S22, 46L57 |
| url | https://arxiv.org/abs/2508.06396 |