{"id":1055,"date":"2016-02-05T12:41:18","date_gmt":"2016-02-05T10:41:18","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/multiqubit-clifford-groups-are-unitary-3-designs\/"},"modified":"2016-02-05T12:41:18","modified_gmt":"2016-02-05T10:41:18","slug":"multiqubit-clifford-groups-are-unitary-3-designs","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/multiqubit-clifford-groups-are-unitary-3-designs\/","title":{"rendered":"Multiqubit Clifford groups are unitary 3-designs"},"content":{"rendered":"<p><span>We show that the multiqubit (including qubit) Clifford group in any even prime power dimension is not only a unitary 2-design, but also a unitary 3-design. Moreover, it is a minimal unitary 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. By contrast, the Clifford group in any odd prime power dimension is only a unitary 2-design. In addition, we show that no operator basis is covariant with respect to any group that is a unitary 3-design, thereby providing a simple explanation of why no discrete Wigner function is covariant with respect to the multiqubit Clifford group.<\/span><\/p>\n<p><span>(http:\/\/arxiv.org\/abs\/1510.02619)<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We show that the multiqubit (including qubit) Clifford group in any even prime power dimension is not only a unitary 2-design, but also a unitary 3-design. Moreover, it is a minimal unitary 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1055","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1055","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=1055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}