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In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability \u2013 despite the fact that the classical random walk returns with certainty \u2013 and we identify the conditions under which this intriguing phenomenon occurs. Numerical evaluation of the first-return generating function allows us to investigate the asymptotics of the return probability as the step number approaches infinity. This provides strong evidence that the suppression of recurrence probability is not a transient effect but a robust feature of the underlying quantum-classical interplay in the asymptotic limit. Our results show that for certain tasks discrete-time quantum stochastic walks outperform both classical random walks and unitary quantum walks.<\/jats:p>","DOI":"10.22331\/q-2026-01-22-1982","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T10:50:39Z","timestamp":1769079039000},"page":"1982","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Recurrence in discrete-time quantum stochastic walks"],"prefix":"10.22331","volume":"10","author":[{"given":"Martin","family":"\u0160tefa\u0148\u00e1k","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1-Star\u00e9 M\u011bsto, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V\u00e1clav","family":"Poto\u010dek","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1-Star\u00e9 M\u011bsto, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u0130skender","family":"Yal\u00e7\u0131nkaya","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1-Star\u00e9 M\u011bsto, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aur\u00e9l","family":"G\u00e1bris","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1-Star\u00e9 M\u011bsto, Czech Republic"},{"name":"Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, 1525 P.O. 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