Monitoring of quantum walks with weak measurements

Quantum Physics [Submitted on 27 Mar 2026] Monitoring of quantum walks with weak measurements Klaus Ziegler, Tim Heine, Sabine Tornow Measurements can be used to monitor the evolution of quantum systems and can give rise to quantized return statistics. It is known that the mean return time is quantized for strong monitoring through the winding number of the monitored quantum state. We discuss that under coherent weak monitoring, implemented via ancilla coupling, the mean return time of a quantum walk obeys a scaling relation with respect to the measurement strength. An analog scaling relation was previously found for random-time monitoring, indicating that weak and random-time monitoring have similar effects. We discuss how weak monitoring via ancilla coupling is linked to the unitary evolution, and how this connection can be controlled by a convergent perturbation theory. Comments: 9 pages, 2 figures Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2603.26933 [quant-ph]   (or arXiv:2603.26933v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26933 Focus to learn more Submission history From: Klaus Ziegler [view email] [v1] Fri, 27 Mar 2026 19:16:24 UTC (50 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.dis-nn References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)