{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T15:52:43Z","timestamp":1773244363938,"version":"3.50.1"},"reference-count":40,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2010,11,8]],"date-time":"2010-11-08T00:00:00Z","timestamp":1289174400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p>In this paper, we consider a discrete-time quantum walk on the<jats:italic>N<\/jats:italic>-cycle governed by the condition that at every time step of the walk, the option persists, with probability<jats:italic>p<\/jats:italic>, of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems corresponding to the space of the coin and the space of the walker must eventually diminish to zero. Put plainly, any level of decoherence greater than zero forces the system to become completely \u2018disentangled\u2019 eventually.<\/jats:p>","DOI":"10.1017\/s096012951000040x","type":"journal-article","created":{"date-parts":[[2010,11,8]],"date-time":"2010-11-08T11:00:45Z","timestamp":1289214045000},"page":"1099-1115","source":"Crossref","is-referenced-by-count":6,"title":["On the von Neumann entropy of certain quantum walks subject to decoherence"],"prefix":"10.1017","volume":"20","author":[{"given":"CHAOBIN","family":"LIU","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NELSON","family":"PETULANTE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,11,8]]},"reference":[{"key":"S096012951000040X_ref40","first-page":"1","volume-title":"Decoherence Poincar\u00e9 Seminar 2005, Progress in Mathematical Physics","author":"Zurek","year":"2003"},{"key":"S096012951000040X_ref39","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/8\/5\/081"},{"key":"S096012951000040X_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-69365-9_7"},{"key":"S096012951000040X_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-009-0930-1"},{"key":"S096012951000040X_ref35","doi-asserted-by":"crossref","DOI":"10.2200\/S00144ED1V01Y200808QMC001","volume-title":"Quantum Walks for Computer Scientists","author":"Venegas-Andraca","year":"2008"},{"key":"S096012951000040X_ref8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.130602"},{"key":"S096012951000040X_ref17","doi-asserted-by":"publisher","DOI":"10.1080\/00107151031000110776"},{"key":"S096012951000040X_ref18","first-page":"1169","article-title":"Decoherence in quantum walks \u2013 a review","volume":"17","author":"Kendon","year":"2006","journal-title":"Mathematical Structures in Computer Science"},{"key":"S096012951000040X_ref20","doi-asserted-by":"crossref","unstructured":"Kendon V. and Tregenna B. (2003a) Decoherence in discrete quantum walks (available at arXiv:quant-ph\/0301182).","DOI":"10.1007\/978-3-540-40968-7_18"},{"key":"S096012951000040X_ref26","unstructured":"Nayak A and Vishwanath A. (2000) Quantum Walk on the Line (available at arXiv:quant-ph\/0010117)."},{"key":"S096012951000040X_ref19","volume-title":"Quantum Communication, Measurement and Computing (QCMC\u201302)","author":"Kendon","year":"2002"},{"key":"S096012951000040X_ref14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.66.052319"},{"key":"S096012951000040X_ref10","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/7\/1\/156"},{"key":"S096012951000040X_ref9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.032304"},{"key":"S096012951000040X_ref30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.042305"},{"key":"S096012951000040X_ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.042316"},{"key":"S096012951000040X_ref37","unstructured":"Watrous J. (2008) Theory of Quantum Information, Lecture notes from Fall 2008, Institute for Quantum Computing, University of Waterloo, Canada."},{"key":"S096012951000040X_ref36","unstructured":"Venegas-Andraca S. E. and Bose S. (2009) Quantum Walk-based Generation of Entanglement Between Two Walkers (available at quant-ph\/0901.3946)."},{"key":"S096012951000040X_ref4","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1145\/380752.380757","volume-title":"Proceedings of the 33rd Annual ACM Symposium on Theory of Computing","author":"Ambainis","year":"2001"},{"key":"S096012951000040X_ref7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.052316"},{"key":"S096012951000040X_ref38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.77.062302"},{"key":"S096012951000040X_ref12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019609420309"},{"key":"S096012951000040X_ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.73.042302"},{"key":"S096012951000040X_ref2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1145\/380752.380758","volume-title":"Proceedings of the 33rd Annual ACM Symposium on Theory of Computing","author":"Aharanov","year":"2001"},{"key":"S096012951000040X_ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.032321"},{"key":"S096012951000040X_ref3","doi-asserted-by":"publisher","DOI":"10.1142\/S0219749903000383"},{"key":"S096012951000040X_ref5","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/43\/7\/075301"},{"key":"S096012951000040X_ref15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.012327"},{"key":"S096012951000040X_ref16","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1103\/PhysRevA.58.915","article-title":"Quantum computation and decision trees","volume":"58","author":"Fahri","year":"1998","journal-title":"Physical Review A"},{"key":"S096012951000040X_ref21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.042315"},{"key":"S096012951000040X_ref23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.74.022310"},{"key":"S096012951000040X_ref24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.031113"},{"key":"S096012951000040X_ref25","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/9\/4\/087"},{"key":"S096012951000040X_ref27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.042306"},{"key":"S096012951000040X_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2004.08.070"},{"key":"S096012951000040X_ref29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.062317"},{"key":"S096012951000040X_ref31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.062129"},{"key":"S096012951000040X_ref32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.74.030301"},{"key":"S096012951000040X_ref33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.65.032310"},{"key":"S096012951000040X_ref34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.80.125309"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096012951000040X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T05:56:45Z","timestamp":1636783005000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096012951000040X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,8]]},"references-count":40,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S096012951000040X"],"URL":"https:\/\/doi.org\/10.1017\/s096012951000040x","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11,8]]}}}