{"id":"https://openalex.org/W4414920958","doi":"https://doi.org/10.1140/epjd/s10053-026-01217-9","title":"Classification of coined quantum walks on the line and comparison to correlated classical random walks","display_name":"Classification of coined quantum walks on the line and comparison to correlated classical random walks","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W4414920958","doi":"https://doi.org/10.1140/epjd/s10053-026-01217-9"},"language":"en","primary_location":{"id":"doi:10.1140/epjd/s10053-026-01217-9","doi":"https://doi.org/10.1140/epjd/s10053-026-01217-9","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/s10053-026-01217-9","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjd/s10053-026-01217-9.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1140/epjd/s10053-026-01217-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036132404","display_name":"Lukas Hantzko","orcid":"https://orcid.org/0000-0002-4918-9639","observed_orcids":["https://orcid.org/0000-0002-4918-9639"]},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lukas Hantzko","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe, 30167, Hannover, Niedersachsen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4918-9639","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe, 30167, Hannover, Niedersachsen, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060474905","display_name":"Lennart Binkowski","orcid":"https://orcid.org/0009-0001-3723-7699","observed_orcids":["https://orcid.org/0009-0001-3723-7699"]},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lennart Binkowski","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe, 30167, Hannover, Niedersachsen, Germany"],"raw_orcid":"https://orcid.org/0009-0001-3723-7699","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstra\u00dfe, 30167, Hannover, Niedersachsen, Germany","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036132404","https://openalex.org/A5060474905"],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":{"value":3790,"currency":"USD","value_usd":3790},"apc_paid":{"value":3790,"currency":"USD","value_usd":3790},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0111619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"80","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discrete-time-quantum-walks","display_name":"discrete-time quantum walks","score":0.9990000128746033},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.5849999785423279},{"id":"https://openalex.org/keywords/distributional-equivalence","display_name":"distributional equivalence","score":0.8389999866485596},{"id":"https://openalex.org/keywords/variance-scaling","display_name":"variance scaling","score":0.6639999747276306},{"id":"https://openalex.org/keywords/ballistic-spreading","display_name":"ballistic spreading","score":0.906000018119812},{"id":"https://openalex.org/keywords/skewness","display_name":"skewness","score":0.6660000085830688},{"id":"https://openalex.org/keywords/quantum-classical-comparison","display_name":"quantum-classical comparison","score":0.6320000290870667}],"concepts":[{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.8191999793052673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7055000066757202},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6079000234603882},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5284000039100647},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.44940000772476196},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4117000102996826},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3571000099182129},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3431999981403351},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30730000138282776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.26440000534057617}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1140/epjd/s10053-026-01217-9","doi":"https://doi.org/10.1140/epjd/s10053-026-01217-9","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/s10053-026-01217-9","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjd/s10053-026-01217-9.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2507.23524","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.23524","pdf_url":"https://arxiv.org/pdf/2507.23524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:edpsciences.org:dkey/10.1140/epjd/s10053-026-01217-9","doi":null,"is_oa":false,"landing_page_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjd/s10053-026-01217-9","pdf_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjd/s10053-026-01217-9","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1140/epjd/s10053-026-01217-9","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2507.23524","doi":"https://doi.org/10.48550/arxiv.2507.23524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.23524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1140/epjd/s10053-026-01217-9","doi":"https://doi.org/10.1140/epjd/s10053-026-01217-9","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjd/s10053-026-01217-9","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjd/s10053-026-01217-9.pdf","source":{"id":"https://openalex.org/S174148793","display_name":"The European Physical Journal D","issn_l":"1434-6060","issn":["1434-6060","1434-6079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal D","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320322379","display_name":"Gottfried Wilhelm Leibniz Universit\u00e4t Hannover","ror":"https://ror.org/0304hq317"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414920958.pdf","grobid_xml":"https://content.openalex.org/works/W4414920958.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4248802760","https://openalex.org/W3106256965","https://openalex.org/W1973321785","https://openalex.org/W2087870970","https://openalex.org/W3081114242","https://openalex.org/W2943713780","https://openalex.org/W7099153902","https://openalex.org/W2525959666","https://openalex.org/W2513443784","https://openalex.org/W2018751242"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"a":[3,44,63,79,117,140],"comprehensive":[4],"classification":[5,184],"of":[6,47,66,84,131,142,153,161,176],"one-dimensional":[7],"coined":[8,68],"quantum":[9,37,50,69,121,144,172,190,200,214],"walks":[10,38,51,70,145,173,198,201,208],"on":[11,16,24],"the":[12,17,57,72,95,105,108,128,150,158,167,177],"infinite":[13],"line,":[14],"focusing":[15],"spatial":[18],"probability":[19],"distributions":[20,169],"they":[21],"induce.":[22],"Building":[23],"prior":[25],"results,":[26],"we":[27,60,89,126,165],"identify":[28],"all":[29,48,67],"initial":[30],"coin":[31,215],"states":[32],"that":[33],"lead":[34],"to":[35,107],"symmetric":[36,49,58,187],"for":[39,94,133,186],"arbitrary":[40],"coins":[41],"and":[42,103,122,146,188],"provide":[43],"bijective":[45,80],"parametrisation":[46,65,81],"modulo":[52,82],"distributional":[53],"equivalence.":[54],"Extending":[55],"beyond":[56],"case,":[59],"also":[61],"give":[62],"surjective":[64],"under":[71],"same":[73],"equivalence":[74,83],"relation,":[75],"as":[76,78,139,192,194],"well":[77,193],"their":[85],"limiting":[86,168,211,219],"distributions.":[87],"Furthermore,":[88],"derive":[90],"corrected":[91],"closed-form":[92],"expressions":[93],"walk":[96],"amplitudes,":[97],"resolving":[98],"inaccuracies":[99],"in":[100],"previous":[101],"literature,":[102],"generalise":[104],"approach":[106,209],"correlated":[109,196,206],"classical":[110,123,154,178],"random":[111,197,207],"walk.":[112],"This":[113],"unified":[114],"framework":[115],"enables":[116],"direct":[118],"comparison":[119],"between":[120],"dynamics.":[124],"Additionally,":[125],"discuss":[127],"asymptotic":[129],"scaling":[130],"variances":[132],"both":[134],"models,":[135],"identifying":[136],"quadratic":[137],"spreading":[138],"hallmark":[141],"non-trivial":[143],"contrasting":[147],"it":[148],"with":[149,174],"linear":[151],"behaviour":[152],"walks,":[155,191],"except":[156],"at":[157],"extremal":[159],"points":[160],"maximal":[162],"correlation.":[163],"Finally,":[164],"compare":[166],"arising":[170],"from":[171],"those":[175],"case.":[179],"Graphical":[180],"abstract":[181],"-":[182,199,213],"compact":[183],"results":[185],"general":[189],"classically":[195,205],"spread":[202],"ballistically":[203],"while":[204],"Gaussian":[210],"distribution":[212],"parameter":[216],"directly":[217],"influence":[218],"distribution\u2019s":[220],"skewness":[221]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}