{"id":313757,"date":"2018-11-06T17:09:56","date_gmt":"2018-11-07T01:09:56","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=313757"},"modified":"2018-11-06T17:09:56","modified_gmt":"2018-11-07T01:09:56","slug":"mutually-unbiased-bases-complex-projective-2-designs","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/mutually-unbiased-bases-complex-projective-2-designs\/","title":{"rendered":"Mutually Unbiased Bases are Complex Projective 2-Designs"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is unknown whether this bound can be achieved for any non-prime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0,1\/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2-designs with angle set {1\/(d+1)}.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is unknown whether this bound can be achieved for any non-prime power dimension. In this paper we demonstrate [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), Adelaide, Australia","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"1740-1744","msr_page_range_start":"1740","msr_page_range_end":"1744","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), Adelaide, 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