{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T21:55:19Z","timestamp":1716501319468},"reference-count":45,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Polish National Science Centre","doi-asserted-by":"crossref","award":["2016\/22\/E\/ST6\/00062"],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004281","name":"Polish National Science Centre","doi-asserted-by":"crossref","award":["2015\/18\/E\/ST2\/ 00327"],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case of minimum error discrimination, we focus on discrimination of measurements with the assistance of entanglement. We provide an alternative proof of the fact that all pairs of distinct von Neumann measurements can be distinguished perfectly (i.e. with the unit success probability) using only a finite number of queries. Moreover, we analytically find the minimal number of queries needed for perfect discrimination. We also show that in this scenario querying the measurements in parallel<\/mml:mtext><\/mml:mrow><\/mml:math> gives the optimal strategy, and hence any possible adaptive methods do not offer any advantage over the parallel scheme. In the unambiguous discrimination scenario, we give the general expressions for the optimal discrimination probabilities with and without the assistance of entanglement. Finally, we show that typical pairs of Haar-random von Neumann measurements can be perfectly distinguished with only two queries.<\/jats:p>","DOI":"10.22331\/q-2021-04-06-425","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T13:38:36Z","timestamp":1617716316000},"page":"425","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Multiple-shot and unambiguous discrimination of von Neumann measurements"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-4739-0400","authenticated-orcid":false,"given":"Zbigniew","family":"Pucha\u0142a","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Ba\u0142tycka 5, 44-100 Gliwice, Poland"},{"name":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0476-7132","authenticated-orcid":false,"given":"\u0141ukasz","family":"Pawela","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Ba\u0142tycka 5, 44-100 Gliwice, Poland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8390-6569","authenticated-orcid":false,"given":"Aleksandra","family":"Krawiec","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Ba\u0142tycka 5, 44-100 Gliwice, Poland"},{"name":"Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9171-1734","authenticated-orcid":false,"given":"Ryszard","family":"Kukulski","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Ba\u0142tycka 5, 44-100 Gliwice, Poland"},{"name":"Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-4946-6835","authenticated-orcid":false,"given":"Micha\u0142","family":"Oszmaniec","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, ul. Wita Stwosza 57, 80-308 Gda\u0144sk, Poland"},{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. 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