Optimal Convergence Rate in the Quantum Zeno Effect for Open Quantum Systems in Infinite Dimensions

Abstract In open quantum systems, the Zeno effect consists in frequent applications of a given operation, e.g., measurement, used to restrict time evolution (due, for example, decoherence) states that are invariant under operation. an abstract setting, sequence is alternating concatenation contraction operator (quantum operation) and $$C_0$$ C 0 -contraction semigroup (time evolution) on Banach space. this paper, we prove optimal convergence rate $$\mathcal {O}(\tfrac{1}{n})$$ O ( 1 n ) by proving explicit error bounds. For that, derive new Chernoff-type $$\sqrt{n}$$ -Lemma, which believe be independent interest. Moreover, generalize result two directions: We weaken assumptions generator, inducing dynamics generated unbounded improve uniform topology. Finally, provide large class examples arising from our assumptions.