Regensburg 2022 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 14: Quantum Foundations

QI 14.4: Vortrag

Freitag, 9. September 2022, 10:30–10:45, H9

Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions — •Tim Möbus and Cambyse Rouzé — Technical University Munich, Germany

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 strongly continuous contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate of order 1/n of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type lemma, which we believe to be of independent interest. Moreover, we generalize the Zeno effect in two directions: We weaken the assumptions on the generator, which induce a 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.