{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T19:01:43Z","timestamp":1791226903674,"version":"4.1.0"},"reference-count":7,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF","award":["CCF-2144219"],"award-info":[{"award-number":["CCF-2144219"]}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"crossref","award":["FA9550-21-1-0040"],"award-info":[{"award-number":["FA9550-21-1-0040"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000879","name":"Sloan Foundation","doi-asserted-by":"crossref","award":["FG-2022-18624"],"award-info":[{"award-number":["FG-2022-18624"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We show that <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">&amp;#x03A9;<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>r<\/mml:mi><mml:mi>d<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mi>&amp;#x03F5;<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> copies of an unknown rank-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>r<\/mml:mi><\/mml:math>, dimension-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math> quantum mixed state are necessary in order to learn a classical description with <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mo>&amp;#x2013;<\/mml:mo><mml:mi>&amp;#x03F5;<\/mml:mi><\/mml:math> fidelity. This improves upon the tomography lower bounds obtained by Haah, et al. and Wright (when closeness is measured with respect to the fidelity function).<\/jats:p>","DOI":"10.22331\/q-2023-01-03-890","type":"journal-article","created":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T14:46:46Z","timestamp":1672757206000},"page":"890","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography"],"prefix":"10.22331","volume":"7","author":[{"given":"Henry","family":"Yuen","sequence":"first","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Dagmar Bru\u00df and Chiara Macchiavello. Optimal state estimation for $d$-dimensional quantum systems. Physics Letters A, 253 (5-6): 249\u2013251, 1999. https:\/\/doi.org\/10.1016\/S0375-9601(99)00099-7.","DOI":"10.1016\/S0375-9601(99)00099-7"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Jeongwan Haah, Aram W Harrow, Zhengfeng Ji, Xiaodi Wu, and Nengkun Yu. Sample-optimal tomography of quantum states. IEEE Transactions on Information Theory, 63 (9): 5628\u20135641, 2017. https:\/\/doi.org\/10.1145\/2897518.2897585.","DOI":"10.1145\/2897518.2897585"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Michael Keyl and Reinhard F Werner. Optimal cloning of pure states, testing single clones. Journal of Mathematical Physics, 40 (7): 3283\u20133299, 1999. https:\/\/doi.org\/10.1063\/1.532887.","DOI":"10.1063\/1.532887"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Ryan O&apos;Donnell and John Wright. Efficient quantum tomography. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 899\u2013912, 2016. https:\/\/doi.org\/10.1145\/2897518.2897544.","DOI":"10.1145\/2897518.2897544"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Reinhard F Werner. Optimal cloning of pure states. Physical Review A, 58 (3): 1827, 1998. https:\/\/doi.org\/10.1103\/PhysRevA.58.1827.","DOI":"10.1103\/PhysRevA.58.1827"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Andreas Winter. Coding theorem and strong converse for quantum channels. IEEE Transactions on Information Theory, 45 (7): 2481\u20132485, 1999. https:\/\/doi.org\/10.1109\/18.796385.","DOI":"10.1109\/18.796385"},{"key":"6","unstructured":"John Wright. How to learn a quantum state. PhD thesis, Carnegie Mellon University, 2016."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-01-03-890\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T12:14:25Z","timestamp":1673352865000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2023-01-03-890\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,3]]},"references-count":7,"URL":"https:\/\/doi.org\/10.22331\/q-2023-01-03-890","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,3]]},"article-number":"890"}}