{"id":"https://openalex.org/W2981628038","doi":"https://doi.org/10.1142/s1230161219500161","title":"Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics","display_name":"Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics","publication_year":2019,"publication_date":"2019-09-01","ids":{"openalex":"https://openalex.org/W2981628038","doi":"https://doi.org/10.1142/s1230161219500161","mag":"2981628038"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161219500161","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161219500161","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065193506","display_name":"Margarita A. Man\u2019ko","orcid":null},"institutions":[{"id":"https://openalex.org/I118517470","display_name":"P.N. Lebedev Physical Institute of the Russian Academy of Sciences","ror":"https://ror.org/01jkd3546","country_code":"RU","type":"facility","lineage":["https://openalex.org/I118517470","https://openalex.org/I1313323035","https://openalex.org/I2800498218","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Margarita A. Man\u2019ko","raw_affiliation_strings":["Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia"],"affiliations":[{"raw_affiliation_string":"Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia","institution_ids":["https://openalex.org/I118517470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056505887","display_name":"V. I. Man\u02b9ko","orcid":"https://orcid.org/0000-0003-3972-0227"},"institutions":[{"id":"https://openalex.org/I118517470","display_name":"P.N. Lebedev Physical Institute of the Russian Academy of Sciences","ror":"https://ror.org/01jkd3546","country_code":"RU","type":"facility","lineage":["https://openalex.org/I118517470","https://openalex.org/I1313323035","https://openalex.org/I2800498218","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir I. Man\u2019ko","raw_affiliation_strings":["Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia"],"affiliations":[{"raw_affiliation_string":"Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia","institution_ids":["https://openalex.org/I118517470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065193506"],"corresponding_institution_ids":["https://openalex.org/I118517470"],"apc_list":null,"apc_paid":null,"fwci":0.28,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66381746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"03","first_page":"1950016","last_page":"1950016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9995999932289124,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9995999932289124,"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":0.9988999962806702,"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/T11414","display_name":"Quantum optics and atomic interactions","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.8290315866470337},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.5775449275970459},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.5581585764884949},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5224456191062927},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.509067952632904},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5088401436805725},{"id":"https://openalex.org/keywords/quantum-superposition","display_name":"Quantum superposition","score":0.48871588706970215},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.48807060718536377},{"id":"https://openalex.org/keywords/probability-amplitude","display_name":"Probability amplitude","score":0.48699551820755005},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47634151577949524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46737924218177795},{"id":"https://openalex.org/keywords/density-of-states","display_name":"Density of states","score":0.457597553730011},{"id":"https://openalex.org/keywords/coherent-states","display_name":"Coherent states","score":0.4151530861854553},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3827984929084778},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.321863055229187},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.29902803897857666}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.8290315866470337},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5775449275970459},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.5581585764884949},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5224456191062927},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.509067952632904},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5088401436805725},{"id":"https://openalex.org/C55615164","wikidata":"https://www.wikidata.org/wiki/Q830791","display_name":"Quantum superposition","level":3,"score":0.48871588706970215},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.48807060718536377},{"id":"https://openalex.org/C94231801","wikidata":"https://www.wikidata.org/wiki/Q653850","display_name":"Probability amplitude","level":5,"score":0.48699551820755005},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47634151577949524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46737924218177795},{"id":"https://openalex.org/C53964469","wikidata":"https://www.wikidata.org/wiki/Q230895","display_name":"Density of states","level":2,"score":0.457597553730011},{"id":"https://openalex.org/C152026323","wikidata":"https://www.wikidata.org/wiki/Q1032070","display_name":"Coherent states","level":3,"score":0.4151530861854553},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3827984929084778},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.321863055229187},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.29902803897857666},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1230161219500161","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161219500161","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W144414008","https://openalex.org/W249485604","https://openalex.org/W2010742203","https://openalex.org/W2029692747","https://openalex.org/W2040517795","https://openalex.org/W2052876372","https://openalex.org/W2056471637","https://openalex.org/W2067346563","https://openalex.org/W2076062749","https://openalex.org/W2142027588","https://openalex.org/W2159136592","https://openalex.org/W2170649178","https://openalex.org/W2170942924","https://openalex.org/W2321378638","https://openalex.org/W2374631013","https://openalex.org/W2524890004","https://openalex.org/W2604146292","https://openalex.org/W2749924903","https://openalex.org/W2771967612","https://openalex.org/W2792466273","https://openalex.org/W2810691835","https://openalex.org/W2888128581","https://openalex.org/W2891147374","https://openalex.org/W2912742595","https://openalex.org/W2963280219","https://openalex.org/W2964134078","https://openalex.org/W3098274590","https://openalex.org/W3098994453","https://openalex.org/W3099426515","https://openalex.org/W3099767593","https://openalex.org/W3099784951","https://openalex.org/W3103099765","https://openalex.org/W3103372800","https://openalex.org/W3104931540","https://openalex.org/W3165898261","https://openalex.org/W4233369467"],"related_works":["https://openalex.org/W1970283688","https://openalex.org/W43906224","https://openalex.org/W2236352299","https://openalex.org/W843425489","https://openalex.org/W2800720047","https://openalex.org/W2023729760","https://openalex.org/W2924097398","https://openalex.org/W2368474868","https://openalex.org/W2355340291","https://openalex.org/W2981437175"],"abstract_inverted_index":{"The":[0,21,49],"superposition":[1],"of":[2,10,15,24,27,36,42,51,57],"pure":[3,47],"quantum":[4],"states":[5,29,38,59],"explicitly":[6],"expressed":[7],"in":[8],"terms":[9],"a":[11,40],"nonlinear":[12],"addition":[13],"rule":[14],"state":[16],"density":[17,25],"operators":[18,53],"is":[19,30,54],"reviewed.":[20],"probability":[22,44],"representation":[23],"matrices":[26],"qudit":[28],"used":[31],"to":[32],"formulate":[33],"the":[34,37,43],"interference":[35],"as":[39],"combination":[41],"distributions":[45],"describing":[46],"states.":[48],"formalism":[50],"quantizer\u2013dequantizer":[52],"developed.":[55],"Examples":[56],"spin-1/2":[58],"and":[60],"f-oscillator":[61],"systems":[62],"are":[63],"considered.":[64]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}