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arXiv · 2111.13911

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

Tim Möbus·Cambyse Rouzé
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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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Tim Möbus, Cambyse Rouzé. 2021-11-27. Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions. https://doi.org/10.1007/s00023-022-01241-6

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