Infinite dimensional dynamical maps
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915776286425088 |
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| author | Bhattacharya, Bihalan Franz, Uwe Patra, Saikat Sengupta, Ritabrata |
| author_facet | Bhattacharya, Bihalan Franz, Uwe Patra, Saikat Sengupta, Ritabrata |
| contents | Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps $\{Λ_t: t \ge 0\}$ is Markovian or non-Markovian. We study the problem when the underlying Hilbert space is of infinite dimensional. We construct a sufficient condition for checking P (resp. CP) divisibility of dynamical maps. We construct several examples where the underlying Hilbert space may not be of finite dimensional. We also give a special emphasis on Gaussian dynamical maps and get a version of our result in it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite dimensional dynamical maps Bhattacharya, Bihalan Franz, Uwe Patra, Saikat Sengupta, Ritabrata Functional Analysis Operator Algebras Quantum Physics 81P40, 81P47, 94A15 Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps $\{Λ_t: t \ge 0\}$ is Markovian or non-Markovian. We study the problem when the underlying Hilbert space is of infinite dimensional. We construct a sufficient condition for checking P (resp. CP) divisibility of dynamical maps. We construct several examples where the underlying Hilbert space may not be of finite dimensional. We also give a special emphasis on Gaussian dynamical maps and get a version of our result in it. |
| title | Infinite dimensional dynamical maps |
| topic | Functional Analysis Operator Algebras Quantum Physics 81P40, 81P47, 94A15 |
| url | https://arxiv.org/abs/2406.19176 |