{"id":"https://openalex.org/W4415968791","doi":"https://doi.org/10.1109/tit.2025.3629670","title":"A Variant of the Bravyi\u2013Terhal Bound for Arbitrary Boundary Conditions","display_name":"A Variant of the Bravyi\u2013Terhal Bound for Arbitrary Boundary Conditions","publication_year":2025,"publication_date":"2025-11-06","ids":{"openalex":"https://openalex.org/W4415968791","doi":"https://doi.org/10.1109/tit.2025.3629670"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2025.3629670","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3629670","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5004451982","display_name":"Franc\u0328ois Arnault","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Arnault","raw_affiliation_strings":["XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397"]},{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019785896","display_name":"Philippe Gaborit","orcid":"https://orcid.org/0000-0002-4034-521X"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Gaborit","raw_affiliation_strings":["XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France"],"raw_orcid":"https://orcid.org/0000-0002-4034-521X","affiliations":[{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397"]},{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092676277","display_name":"Wouter Rozendaal","orcid":"https://orcid.org/0009-0004-8290-6136"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wouter Rozendaal","raw_affiliation_strings":["IMB, UMR 5251, Universit&#x00E9; de Bordeaux, Talence, France","IMB, UMR 5251, Universit&#x00E9; de Bordeaux, 351, Cours de la Lib&#x00E9;ration, Talence, France"],"raw_orcid":"https://orcid.org/0009-0004-8290-6136","affiliations":[{"raw_affiliation_string":"IMB, UMR 5251, Universit&#x00E9; de Bordeaux, Talence, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530"]},{"raw_affiliation_string":"IMB, UMR 5251, Universit&#x00E9; de Bordeaux, 351, Cours de la Lib&#x00E9;ration, Talence, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116129054","display_name":"Nicolas Saussay","orcid":"https://orcid.org/0009-0002-4480-6236"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Saussay","raw_affiliation_strings":["XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France"],"raw_orcid":"https://orcid.org/0009-0002-4480-6236","affiliations":[{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, Limoges, France","institution_ids":["https://openalex.org/I4210093397"]},{"raw_affiliation_string":"XLIM, UMR 7252, Universit&#x00E9; de Limoges, 123, Avenue Albert Thomas, Limoges, France","institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064676731","display_name":"Gilles Z\u00e9mor","orcid":"https://orcid.org/0000-0002-6041-9554"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Z\u00e9mor","raw_affiliation_strings":["IMB, UMR 5251, Universit&#x00E9; de Bordeaux, Talence, France","IMB, UMR 5251, Universit&#x00E9; de Bordeaux, 351, Cours de la Lib&#x00E9;ration, Talence, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMB, UMR 5251, Universit&#x00E9; de Bordeaux, Talence, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530"]},{"raw_affiliation_string":"IMB, UMR 5251, Universit&#x00E9; de Bordeaux, 351, Cours de la Lib&#x00E9;ration, Talence, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004451982"],"corresponding_institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16586838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"1","first_page":"437","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8885999917984009,"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":0.8885999917984009,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.05000000074505806,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6467000246047974},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6100999712944031},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5526999831199646},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.4309000074863434},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.3962000012397766},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.3822999894618988},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.3822999894618988},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.37439998984336853},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.3643999993801117}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7526999711990356},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6467000246047974},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6100999712944031},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5347999930381775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4900999963283539},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.4309000074863434},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.37439998984336853},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.32679998874664307},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3230000138282776},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C120047569","wikidata":"https://www.wikidata.org/wiki/Q92795049","display_name":"Group algebra","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26829999685287476},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.2637999951839447},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C95627345","wikidata":"https://www.wikidata.org/wiki/Q1138961","display_name":"Quotient group","level":4,"score":0.2542000114917755},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3629670","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3629670","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W196044395","https://openalex.org/W1956864028","https://openalex.org/W2003457205","https://openalex.org/W2009989296","https://openalex.org/W2042474962","https://openalex.org/W2062794279","https://openalex.org/W2088636071","https://openalex.org/W2092838737","https://openalex.org/W2100990159","https://openalex.org/W2114207424","https://openalex.org/W2119314900","https://openalex.org/W2135273380","https://openalex.org/W3172819695","https://openalex.org/W3206809046","https://openalex.org/W3213933684","https://openalex.org/W3216521614","https://openalex.org/W4206558398","https://openalex.org/W4226332664","https://openalex.org/W4313227180","https://openalex.org/W4391530691","https://openalex.org/W4393234688","https://openalex.org/W4403119452","https://openalex.org/W4404040855"],"related_works":[],"abstract_inverted_index":{"We":[0,84,145],"present":[1],"a":[2,20,29,67,98,180,184],"modified":[3],"version":[4],"of":[5,34,38,49,58,66,100,110,159,179],"the":[6,104,111,139,156,170],"Bravyi-Terhal":[7],"bound":[8,149,154],"that":[9,55,86],"applies":[10],"to":[11,150],"quantum":[12],"codes":[13,165],"defined":[14],"by":[15],"local":[16],"parity-check":[17,167],"constraints":[18],"on":[19,92,155],"<italic":[21,45,62,70,77,81,107,114,118,126,140],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[22,32,36,46,51,63,71,78,82,108,115,119,123,127,132,136,141],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>-dimensional":[23,47,142],"lattice":[24],"quotient.":[25],"Specifically,":[26],"we":[27,53],"consider":[28],"quotient":[30,60],"Z<italic":[31,35,50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sup>D</sup></i>/\u039b":[33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sup>D</sup></i>":[37],"cardinality":[39],"\u2113,":[40],"where":[41,134],"\u039b":[42],"is":[43,138],"some":[44],"sublattice":[48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sup>D</sup></i>:":[52],"suppose":[54],"every":[56],"vertex":[57],"this":[59,148],"indexes":[61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</i>":[64,120],"qubits":[65,93],"stabilizer":[68,89],"code":[69,112],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</i>,":[72],"which":[73],"therefore":[74],"has":[75],"length":[76],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[79],"=":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</i>\u2113.":[83],"prove":[85],"if":[87],"all":[88],"generators":[90],"act":[91],"whose":[94,166],"indices":[95],"lie":[96],"within":[97],"ball":[99],"radius":[101],"\u03c1,":[102],"then":[103,146],"minimum":[105,157],"distance":[106,158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</i>":[109,116],"satisfies":[113],"\u2264":[117],"\u221a":[121,125],"\u03b3<italic":[122,135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>(":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[128],"+":[129],"4\u03c1)\u2113":[130],"<sup":[131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>D</i>\u22121/<i>D</i></sup>,":[133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><sub>D</sub></i>":[137],"Hermite":[143],"constant.":[144],"apply":[147],"derive":[151],"an":[152,177],"upper":[153],"Abelian":[160],"Two-Block":[161],"Group":[162],"Algebra":[163],"(2BGA)":[164],"matrices":[168],"have":[169],"form":[171],"[A|B]":[172],"with":[173],"each":[174],"submatrix":[175],"representing":[176],"element":[178],"group":[181],"algebra":[182],"over":[183],"finite":[185],"abelian":[186],"group.":[187]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-11-06T00:00:00"}
