{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T15:14:34Z","timestamp":1760800474919,"version":"3.40.5"},"reference-count":37,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T00:00:00Z","timestamp":1619395200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"crossref","award":["DEC-2015\/18\/A\/ST2\/00274"],"award-info":[{"award-number":["DEC-2015\/18\/A\/ST2\/00274"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"crossref","award":["2019\/35\/O\/ST2\/01049"],"award-info":[{"award-number":["2019\/35\/O\/ST2\/01049"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"crossref","award":["Team-Net NTQC project"],"award-info":[{"award-number":["Team-Net NTQC project"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We analyse orthogonal bases in a composite <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math> Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>N<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:math> reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math> of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:math> and provide a general construction of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>N<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:math> states forming such an optimal basis in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">H<\/mml:mi><\/mml:mrow><mml:mi>N<\/mml:mi><\/mml:msub><mml:mo>\u2297<\/mml:mo><mml:msub><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">H<\/mml:mi><\/mml:mrow><mml:mi>N<\/mml:mi><\/mml:msub><\/mml:math>. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.<\/jats:p>","DOI":"10.22331\/q-2021-04-26-442","type":"journal-article","created":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T13:31:49Z","timestamp":1619443909000},"page":"442","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Bipartite quantum measurements with optimal single-sided distinguishability"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4062-833X","authenticated-orcid":false,"given":"Jakub","family":"Czartowski","sequence":"first","affiliation":[{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0653-3639","authenticated-orcid":false,"given":"Karol","family":"\u017byczkowski","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"},{"name":"Centrum Fizyki Teoretycznej PAN, Al. Lotnik\u00f3w 32\/46, 02-668 Warszawa, Poland"},{"name":"National Quantum Information Center (KCIK), University of Gda\u0144sk, Poland"}]}],"member":"9598","published-online":{"date-parts":[[2021,4,26]]},"reference":[{"key":"0","doi-asserted-by":"crossref","unstructured":"A. Peres, Quantum Theory: Concepts and Methods. Springer, 1995.","DOI":"10.1119\/1.17946"},{"key":"1","doi-asserted-by":"crossref","unstructured":"I. Bengtsson and K. \u017byczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, II ed. Cambridge University Press, 2017.","DOI":"10.1017\/9781139207010"},{"key":"2","doi-asserted-by":"publisher","unstructured":"4 J. S. Bell, ``On the problem of hidden variables in quantum mechanics,'' Rev. Mod. Phys., vol. 38, pp. 447\u2013452, 1966. URL: https:\/\/doi.org\/10.1103\/RevModPhys.38.447 0pt.","DOI":"10.1103\/RevModPhys.38.447"},{"key":"3","doi-asserted-by":"publisher","unstructured":"4 N. Gisin and H. 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