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In open quantum systems, the quantum Zeno effect consists in frequentapplications of a given quantum operation, e.g.~a measurement, used to restrictthe time evolution (due e.g.~to decoherence) to states that are invariant underthe quantum operation. In an abstract setting, the Zeno sequence is analternating 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 Zenosequence by proving explicit error bounds. For that, we derive a newChernoff-type $\sqrt{n}$-Lemma, which we believe to be of independent interest.Moreover, we generalize the convergence result for the Zeno effect in twodirections: We weaken the assumptions on the generator, inducing the Zenodynamics generated by an unbounded generator and we improve the convergence tothe uniform topology. Finally, we provide a large class of examples arisingfrom our assumptions.

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