{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T10:42:16Z","timestamp":1776940936297,"version":"3.51.4"},"reference-count":66,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T00:00:00Z","timestamp":1624406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["200021 156672"],"award-info":[{"award-number":["200021 156672"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between \u201cquantum discord\u201d and \u201casymmetric relative entropy of discord\u201d: the former never exceeds the latter. We also prove that for all BDS the two coincide.<\/jats:p>","DOI":"10.3390\/e23070797","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T11:28:41Z","timestamp":1624447721000},"page":"797","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4143-9207","authenticated-orcid":false,"given":"Elias","family":"Riedel G\u00e5rding","sequence":"first","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"},{"name":"Department of Physics, Royal Institute of Technology (KTH), 100 44 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0456-3308","authenticated-orcid":false,"given":"Nicolas","family":"Schwaller","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun Lam","family":"Chan","sequence":"additional","affiliation":[{"name":"Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5768-2434","authenticated-orcid":false,"given":"Su Yeon","family":"Chang","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samuel","family":"Bosch","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"},{"name":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frederic","family":"Gessler","sequence":"additional","affiliation":[{"name":"Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Willy Robert","family":"Laborde","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"},{"name":"School of Physics, AMBER and CRANN Institute, Trinity College Dublin, The University of Dublin, College Green, Dublin 2, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier Naya","family":"Hernandez","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"},{"name":"School of Science and Engineering, Tecnol\u00f3gico de Monterrey, Monterrey 64849, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyu","family":"Si","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc-Andr\u00e9","family":"Dupertuis","sequence":"additional","affiliation":[{"name":"Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Macris","sequence":"additional","affiliation":[{"name":"Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1137\/S0097539795293172","article-title":"Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer","volume":"26","author":"Shor","year":"1997","journal-title":"SIAM J. 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