Law of large numbers and central limit theorem for ergodic quantum processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911198768791552 |
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| author | Pathirana, Lubashan Schenker, Jeffrey |
| author_facet | Pathirana, Lubashan Schenker, Jeffrey |
| contents | A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Law of large numbers and central limit theorem for ergodic quantum processes Pathirana, Lubashan Schenker, Jeffrey Mathematical Physics Probability Quantum Physics A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum operation with noise. Such ergodic quantum processes generalize independent quantum processes. An ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility and mixing conditions, we obtain a central limit type theorem describing fluctuations around the ergodic limit. |
| title | Law of large numbers and central limit theorem for ergodic quantum processes |
| topic | Mathematical Physics Probability Quantum Physics |
| url | https://arxiv.org/abs/2303.08992 |