{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T01:48:11Z","timestamp":1773539291183,"version":"3.50.1"},"reference-count":41,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T00:00:00Z","timestamp":1500595200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Z<\/mml:mi><\/mml:math>and -<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><\/mml:math>bases. This strategy was recently shown to achieve an approximate unitary<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><\/mml:math>-design after a number of repetitions of the process, which implies that the strategy gradually achieves decoupling. Here, we prove that even fewer repetitions of the process achieve decoupling at the same rate as that with the uniform ones, showing that rather imprecise approximations of unitary<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>2<\/mml:mn><\/mml:math>-designs are sufficient for decoupling. We also briefly discuss efficient implementations of them and implications of our decoupling theorem to coherent state merging and relative thermalisation.<\/jats:p>","DOI":"10.22331\/q-2017-07-21-18","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T09:51:56Z","timestamp":1500630716000},"page":"18","source":"Crossref","is-referenced-by-count":11,"title":["Decoupling with random diagonal unitaries"],"prefix":"10.22331","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1285-6968","authenticated-orcid":false,"given":"Yoshifumi","family":"Nakata","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstrasse 2, 30167 Hannover, Germany."},{"name":"Photon Science Center, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan."},{"name":"Departament de F\u00edsica: Grup d\u2019Informaci\u00f3 Qu\u00e0ntica, Universitat Aut\u00f2noma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Hirche","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstrasse 2, 30167 Hannover, Germany."},{"name":"Departament de F\u00edsica: Grup d\u2019Informaci\u00f3 Qu\u00e0ntica, Universitat Aut\u00f2noma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ciara","family":"Morgan","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Appelstrasse 2, 30167 Hannover, Germany."},{"name":"School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4. 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