{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:24:21Z","timestamp":1778019861026,"version":"3.51.4"},"reference-count":56,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12234013"],"award-info":[{"award-number":["12234013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12174221"],"award-info":[{"award-number":["12174221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider the first detection problem for a one-dimensional quantum walk with repeated local measurements. Employing the stroboscopic projective measurement protocol and the renewal equation, we study the effect of tunneling on the detection time. Specifically, we study the continuous-time quantum walk on an infinite tight-binding lattice for two typical situations with physical reality. The first is the case of a quantum walk in the absence of tunneling with a Gaussian initial state. The second is the case where a barrier is added to the system. It is shown that the transition of the decay behavior of the first detection probability can be observed by modifying the initial condition, and in the presence of a tunneling barrier, the particle can be detected earlier than the impurity-free lattice. This suggests that the evolution of the walker is expedited when it tunnels through the barrier under repeated measurement. The first detection tunneling time is introduced to investigate the tunneling time of the quantum walk. In addition, we analyze the critical transitive point by deriving an asymptotic formula.<\/jats:p>","DOI":"10.3390\/e25081231","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T10:14:38Z","timestamp":1692353678000},"page":"1231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["First Detection and Tunneling Time of a Quantum Walk"],"prefix":"10.3390","volume":"25","author":[{"given":"Zhenbo","family":"Ni","sequence":"first","affiliation":[{"name":"School of Physics, Shandong University, Jinan 250100, China"},{"name":"Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yujun","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Physics, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hughes, B.D. 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