{"id":313751,"date":"2018-11-06T17:09:59","date_gmt":"2018-11-07T01:09:59","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=313751"},"modified":"2018-11-06T17:09:59","modified_gmt":"2018-11-07T01:09:59","slug":"implementation-group-covariant-povms-orthogonal-measurements","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/implementation-group-covariant-povms-orthogonal-measurements\/","title":{"rendered":"Implementation of Group-Covariant POVMs by Orthogonal Measurements"},"content":{"rendered":"

We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark’s theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to find an implementation of a given group-covariant POVM by a quantum circuit using its symmetry. Based on representation theory of the symmetry group we develop a general approach for the implementation of group-covariant POVMs which consist of rank-one operators. The construction relies on a method to decompose matrices that intertwine two representations of a finite group. We give several examples for which the resulting quantum circuits are efficient. In particular, we obtain efficient quantum circuits for a class of POVMs generated by Weyl-Heisenberg groups. These circuits allow to implement an approximative simultaneous measurement of the position and crystal momentum of a particle moving on a cyclic chain.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark’s theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to find an implementation of a given group-covariant POVM by a quantum circuit using its symmetry. Based on representation theory of […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[243138],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-313751","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2004-07-07","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"Journal of Mathematical Physics","msr_volume":"46","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"459228","msr_publicationurl":"https:\/\/arxiv.org\/abs\/quant-ph\/0407054","msr_doi":"10.1063\/1.1827924","msr_publication_uploader":[{"type":"file","title":"Implementation of Group-Covariant POVMs by Orthogonal Measurements","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2016\/11\/Implementation-of-Group-Covariant-POVMs-by-Orthogonal-Measurements-.pdf","id":459228,"label_id":0},{"type":"url","title":"https:\/\/arxiv.org\/abs\/quant-ph\/0407054","viewUrl":false,"id":false,"label_id":0},{"type":"doi","title":"10.1063\/1.1827924","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/abs\/quant-ph\/0407054"}],"msr-author-ordering":[{"type":"text","value":"Thomas Decker","user_id":0,"rest_url":false},{"type":"text","value":"Dominik Janzing","user_id":0,"rest_url":false},{"type":"user_nicename","value":"martinro","user_id":32823,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=martinro"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"article","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/313751"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/313751\/revisions"}],"predecessor-version":[{"id":521242,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/313751\/revisions\/521242"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=313751"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=313751"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=313751"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=313751"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=313751"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=313751"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=313751"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=313751"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=313751"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=313751"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=313751"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=313751"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=313751"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=313751"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=313751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}