Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions (2111.13911v4)

Published 27 Nov 2021 in quant-ph, math-ph, math.MP, and math.SP

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.

Summary

We haven't generated a summary for this paper yet.