Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913742932934656 |
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| author | Möbus, Tim Rouzé, Cambyse |
| author_facet | Möbus, Tim Rouzé, Cambyse |
| contents | In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation, e.g.~a measurement, used to restrict the time evolution (due e.g.~to decoherence) to states that are invariant under the quantum operation. In an abstract setting, the Zeno sequence is an alternating concatenation of a contraction operator (quantum operation) and a $C_0$-contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate of order $\tfrac{1}{n}$ of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type $\sqrt{n}$-Lemma, which we believe to be of independent interest. Moreover, we generalize the convergence result for the Zeno effect in two directions: We weaken the assumptions on the generator, inducing the Zeno dynamics generated by an unbounded generator and we improve the convergence to the uniform topology. Finally, we provide a large class of examples arising from our assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_13911 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions Möbus, Tim Rouzé, Cambyse Quantum Physics Mathematical Physics Spectral Theory In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation, e.g.~a measurement, used to restrict the time evolution (due e.g.~to decoherence) to states that are invariant under the quantum operation. In an abstract setting, the Zeno sequence is an alternating concatenation of a contraction operator (quantum operation) and a $C_0$-contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate of order $\tfrac{1}{n}$ of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type $\sqrt{n}$-Lemma, which we believe to be of independent interest. Moreover, we generalize the convergence result for the Zeno effect in two directions: We weaken the assumptions on the generator, inducing the Zeno dynamics generated by an unbounded generator and we improve the convergence to the uniform topology. Finally, we provide a large class of examples arising from our assumptions. |
| title | Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions |
| topic | Quantum Physics Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2111.13911 |