{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:08:26Z","timestamp":1760234906177,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP19K03616"],"award-info":[{"award-number":["JP19K03616"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Dressed Photon Research Origin","award":["--"],"award-info":[{"award-number":["--"]}]},{"name":"MSMT RVO 14000","award":["--"],"award-info":[{"award-number":["--"]}]},{"DOI":"10.13039\/501100020134","name":"Programma Operativo Nazionale Ricerca e Competitivit\u00e0","doi-asserted-by":"publisher","award":["02.1.01\/0.0\/0.0\/16\\_019\/000077"],"award-info":[{"award-number":["02.1.01\/0.0\/0.0\/16\\_019\/000077"]}],"id":[{"id":"10.13039\/501100020134","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in graph theory.<\/jats:p>","DOI":"10.3390\/sym13071169","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T22:39:43Z","timestamp":1625006383000},"page":"1169","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs"],"prefix":"10.3390","volume":"13","author":[{"given":"Norio","family":"Konno","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Yokohama National University, Yokohama 240-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Etsuo","family":"Segawa","sequence":"additional","affiliation":[{"name":"Graduate School of Environment Information Sciences, Yokohama National University, Yokohama 240-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0433-7765","authenticated-orcid":false,"given":"Martin","family":"\u0160tefa\u0148\u00e1k","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, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1142\/S0219749903000383","article-title":"Quantum walks and their algorithmic applications","volume":"1","author":"Ambainis","year":"2003","journal-title":"Int. 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Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"042129","DOI":"10.1103\/PhysRevA.99.042129","article-title":"Percolated quantum walks with a general shift operator: From trapping to transport","volume":"99","author":"Jex","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"032113","DOI":"10.1103\/PhysRevA.101.032113","article-title":"A counterintuitive role of geometry in transport by quantum walks","volume":"101","author":"Jex","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"126302","DOI":"10.1016\/j.physleta.2020.126302","article-title":"Quantum walk transport on carbon nanotube structures","volume":"384","author":"Jex","year":"2020","journal-title":"Phys. Lett. A"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ohtsu, M., Kobayashi, K., Kawazoe, T., Yatsui, T., and Naruse, M. (2008). Principles of Nanophotonics, Taylor and Francis.","DOI":"10.1201\/9781584889731"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00340-010-3977-y","article-title":"Structural dependency of optical excitation transfer via optical near-field interactions between semiconductor quantum dots","volume":"100","author":"Nomura","year":"2010","journal-title":"Appl. Phys. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"032341","DOI":"10.1103\/PhysRevA.73.032341","article-title":"Hitting time for quantum walks on the hypercube","volume":"73","author":"Krovi","year":"2006","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"042334","DOI":"10.1103\/PhysRevA.74.042334","article-title":"Quantum walks with infinite hitting times","volume":"74","author":"Krovi","year":"2006","journal-title":"Phys. Rev. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4197","DOI":"10.1016\/j.jfa.2014.09.003","article-title":"Spectral and asymptotic properties of Grover walks on crystal lattices","volume":"267","author":"Higuchi","year":"2014","journal-title":"J. Funct. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1090\/conm\/381\/07092","article-title":"Quantum walks on graphs and quantum scattering theory","volume":"Volume 381","author":"Evans","year":"2005","journal-title":"Coding Theory and Quantum Computing (Contemporary Mathematics)"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11343","DOI":"10.1088\/1751-8113\/40\/37\/011","article-title":"Modifying quantum walks: A scattering theory approach","volume":"40","author":"Feldman","year":"2007","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_18","unstructured":"Robinson, M. (1995). Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, CRC Press."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1088\/1751-8121\/ab370b","article-title":"Dynamical system induced by quantum walks","volume":"52","author":"Higuchi","year":"2019","journal-title":"J. Phys. A Math. 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