Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions

• URL: http://arxiv.org/abs/2111.13911v4
• Date: Wed, 5 Oct 2022 12:01:21 GMT
• Title: Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions
• Authors: Tim M\"obus and Cambyse Rouz\'e
• Abstract summary: In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation. We prove the optimal convergence rate of order $tfrac1n$ of the Zeno sequence by proving explicit error bounds. We generalize the convergence result for the Zeno effect in two directions.
• Score: 1.5229257192293197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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