{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T13:27:29Z","timestamp":1780061249238,"version":"3.54.0"},"reference-count":57,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"1","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"name":"Swiss National Science Foundation within the National Centre of Competence in Research through the Project entitled Quantum Science and Technology","award":["200020-135048"],"award-info":[{"award-number":["200020-135048"]}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["258932"],"award-info":[{"award-number":["258932"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ETH","award":["ETH-15 12-2"],"award-info":[{"award-number":["ETH-15 12-2"]}]},{"name":"HYCON2 Project through the Network of Excellence"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1109\/tit.2015.2503755","type":"journal-article","created":{"date-parts":[[2015,11,25]],"date-time":"2015-11-25T19:07:33Z","timestamp":1448478453000},"page":"578-598","source":"Crossref","is-referenced-by-count":24,"title":["Efficient Approximation of Quantum Channel Capacities"],"prefix":"10.1109","volume":"62","author":[{"given":"David","family":"Sutter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tobias","family":"Sutter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peyman","family":"Mohajerin Esfahani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renato","family":"Renner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1137\/110826102"},{"key":"ref38","author":"cover","year":"2006","journal-title":"Elements of Information Theory"},{"key":"ref33","article-title":"Computational complexity certification of gradient methods for real-time model predictive control","author":"richter","year":"0"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1142\/p665"},{"key":"ref31","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","author":"nesterov","year":"2004","journal-title":"Introductory Lectures on Convex Optimization A Basic Course"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/5\/L01"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-155-8_12"},{"key":"ref36","author":"anderson","year":"1987","journal-title":"Linear Programming in Infinite-Dimensional Spaces Theory and Applications"},{"key":"ref35","volume":"2","author":"fremlin","year":"2010","journal-title":"Measure Theory"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719574"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646490"},{"key":"ref27","article-title":"On the duality of strong convexity and strong smoothness: Learning applications and matrix regularization","author":"kakade","year":"0"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/28\/S18"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139525343"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2401002"},{"key":"ref22","author":"bertsekas","year":"2009","journal-title":"Convex Optimization Theory"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.108.171"},{"key":"ref24","first-page":"179","article-title":"On capacities of quantum channels","volume":"17","author":"ohya","year":"1997","journal-title":"Probab Math Statist"},{"key":"ref23","doi-asserted-by":"crossref","DOI":"10.1515\/9781400833344","author":"bernstein","year":"2009","journal-title":"Matrix Mathematics"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-015-2382-0"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.63.022308"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2001.936139"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2215575"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/0100000064","article-title":"Concentration of measure inequalities in information theory, communications and coding","volume":"10","author":"raginsky","year":"2013","journal-title":"Found Trends Commun Inf Theory"},{"key":"ref56","article-title":"Quantum channels & operations","author":"wolf","year":"0"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/132"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.839515"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/s11122-004-0002-2"},{"key":"ref10","first-page":"107","article-title":"Algorithms of Arimoto–Blahut type for computing quantum channel capacity","author":"nagaoka","year":"1999","journal-title":"Proc 2nd QIT"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1224"},{"key":"ref40","first-page":"1","article-title":"First-order methods of smooth convex optimization with inexact oracle","volume":"146","author":"devolder","year":"2013","journal-title":"Math Program"},{"key":"ref12","article-title":"On the complexity of computing zeroerror and Holevo capacity of quantum channels","author":"beigi","year":"2008"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1145\/2432622.2432625"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s10107-003-0446-y","article-title":"Capacities of quantum channels and how to find them","volume":"97","author":"shor","year":"2003","journal-title":"Math Program"},{"key":"ref15","first-page":"2583","article-title":"Numerical experiments on the capacity of quantum channel with entangled input states","volume":"e84 a","author":"osawa","year":"2001","journal-title":"IEICE Trans Fundam Electron Commun Comput Sci"},{"key":"ref16","first-page":"13","article-title":"Qubit channels which require four inputs to achieve capacity: Implications for additivity conjectures","volume":"5","author":"hayashi","year":"2005","journal-title":"Quantum Inf Comput"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0552-5"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-011-9099-z"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/18.651037"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1515\/9783110273403"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1972.1054855"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.56.131"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/ITW.2004.1405276"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1972.1054753"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.042309"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.1998.708959"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1063\/1.3595693"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.022308"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.3824"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2013.835812"},{"key":"ref42","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4145-2","author":"robert","year":"2004","journal-title":"Monte Carlo Statistical Methods (Springer Texts in Statistics)"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-009-0833-1"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1063\/1.1500791"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20135"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/7360961\/7337416.pdf?arnumber=7337416","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T15:58:00Z","timestamp":1642003080000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7337416\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":57,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.1109\/tit.2015.2503755","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}