{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T06:20:24Z","timestamp":1772000424899,"version":"3.50.1"},"reference-count":30,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"6","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"publisher","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundaci\u00f3 Cellex"},{"DOI":"10.13039\/501100003329","name":"Spanish MINECO","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002809","name":"Generalitat de Catalunya (Suport a grups de recerca (SGR)-1381 and Centres de Recerca de Catalunya","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Union under Horizon2020","doi-asserted-by":"publisher","award":["PROBIST 754510"],"award-info":[{"award-number":["PROBIST 754510"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science through TEAM-NET","doi-asserted-by":"publisher","award":["POIR.04.04.00-00-17C1\/18-00"],"award-info":[{"award-number":["POIR.04.04.00-00-17C1\/18-00"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Spanish MINECO funded by FEDER funds","doi-asserted-by":"publisher","award":["FIS2016-86681-P"],"award-info":[{"award-number":["FIS2016-86681-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Spanish MINECO funded by FEDER funds","doi-asserted-by":"publisher","award":["PID2019-107609GB-I00\/AEI\/10.13039\/501100011033"],"award-info":[{"award-number":["PID2019-107609GB-I00\/AEI\/10.13039\/501100011033"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002809","name":"Generalitat de Catalunya","doi-asserted-by":"publisher","award":["2017-SGR-1127"],"award-info":[{"award-number":["2017-SGR-1127"]}],"id":[{"id":"10.13039\/501100002809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1109\/tit.2022.3149291","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T21:08:05Z","timestamp":1644268085000},"page":"3942-3950","source":"Crossref","is-referenced-by-count":53,"title":["Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes"],"prefix":"10.1109","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3720-5195","authenticated-orcid":false,"given":"Markus","family":"Grassl","sequence":"first","affiliation":[{"name":"International Centre for Theory of Quantum Technologies, University of Gdansk, Gda&#x0144;sk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3856-4018","authenticated-orcid":false,"given":"Felix","family":"Huber","sequence":"additional","affiliation":[{"name":"ICFO&#x2014;Institut de Ci&#x00E8;ncies Fot&#x00F2;niques, Castelldefels, Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6344-4870","authenticated-orcid":false,"given":"Andreas","family":"Winter","sequence":"additional","affiliation":[{"name":"Departament de F&#x00ED;sica, Grup d&#x2019;Informaci&#x00F3; Qu&#x00E0;ntica, Universitat Aut&#x00F2;noma de Barcelona, Bellaterra, Barcelona, Spain"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.56.33"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1964.1053661"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.55.900"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/18.782103"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2007.0028"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.3824"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.22331\/q-2020-06-18-284"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1126\/science.1131563"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2313559"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1019653202562","article-title":"Approximate quantum error correction","volume":"1","author":"Schumacher","year":"2002","journal-title":"Quantum Inf. Process."},{"key":"ref11","article-title":"Limitations of noisy reversible computation","author":"Aharonov","year":"1996","journal-title":"arXiv:quant-ph\/9611028"},{"key":"ref12","article-title":"CB-norm estimates for maps between noncommutative $L_{p}$\n-spaces and quantum channel theory","author":"Junge","year":"2014","journal-title":"arXiv:1407.7684"},{"key":"ref13","article-title":"Relative entropy convergence for depolarizing channels","author":"M\u00fcller-Hermes","year":"2015","journal-title":"arXiv:1508.07021"},{"key":"ref14","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.103.L020601","article-title":"Entanglement-assisted quantum communication beating the quantum Singleton bound","volume-title":"16th Asian Quantum Inf. Sci. Conf. (AQIS)","author":"Grassl"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.103.L020601"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928980"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-021-03174-1"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2711601"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s12095-021-00532-9"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.77.064302"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2789347"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.86.032319"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-019-2234-5"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-021-03066-4"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/18.681316"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(00)00480-1"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2053903"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646490"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/28\/S18"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-016-2609-8"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/9778940\/09705292.pdf?arnumber=9705292","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,17]],"date-time":"2024-01-17T22:50:19Z","timestamp":1705531819000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9705292\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":30,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.1109\/tit.2022.3149291","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6]]}}}