{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T15:17:01Z","timestamp":1783696621936,"version":"3.55.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004909","name":"Universidade Federal do Rio Grande do Sul","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004909","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004909","name":"Universidade Federal Do Rio Grande Do Sul","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004909","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"abstract":"Abstract<\/jats:title>\n \n In this paper, we study the recurrence of Open Quantum Walks induced by finite-dimensional coins on the line (\n \n \n $$\\mathbb {Z}$$<\/jats:tex-math>\n \n Z<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ) and on the grid (\n \n \n $$\\mathbb {Z}^2$$<\/jats:tex-math>\n \n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ). Two versions are considered: discrete-time open quantum walks (OQW) and continuous-time open quantum walks (CTOQW). We present three distinct recurrence criteria for OQWs on\n \n \n $$\\mathbb {Z}$$<\/jats:tex-math>\n \n Z<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , each adapted to different types of coins. The first criterion applies to coins whose auxiliary map has a unique invariant state, resulting in the first recurrence criterion for Lazy OQWs. The second applies to Lazy OQWs of dimension 2, where we provide a complete characterization of the recurrence for this low-dimensional case. The third one presents a general criterion for finite-dimensional coins in the non-lazy case, which generalizes several of the previously known results for OQWs on\n \n \n $$\\mathbb {Z}$$<\/jats:tex-math>\n \n Z<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . Also, we present a general recurrence criterion for OQWs on\n \n \n $$\\mathbb {Z}^2$$<\/jats:tex-math>\n \n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n via the open quantum jump chain, obtained from a recurrence criterion for CTOQWs on\n \n \n $$\\mathbb {Z}^2$$<\/jats:tex-math>\n \n \n \n Z<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n .\n <\/jats:p>","DOI":"10.1007\/s11128-026-05180-7","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T05:54:38Z","timestamp":1777442078000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Recurrence criteria for reducible homogeneous open quantum walks on the line and on the grid"],"prefix":"10.1007","volume":"25","author":[{"given":"Newton","family":"Loebens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,29]]},"reference":[{"key":"5180_CR1","doi-asserted-by":"crossref","unstructured":"Attal, S., Guillotin-Plantard, N., Sabot, C.: Central limit theorems for open quantum random walks and quantum measurement records. 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