In this chapter we mention some topics in which the theory of finite fields is applied in quantum information theory. The applications include (i) mutually unbiased bases, (ii) positive operator-valued measures, (iii) quantum error-correcting codes, (iv) period finding, (v) quantum function reconstruction, and (vi) other connections.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this chapter we mention some topics in which the theory of finite fields is applied in quantum information theory. The applications include (i) mutually unbiased bases, (ii) positive operator-valued measures, (iii) quantum error-correcting codes, (iv) period finding, (v) quantum function reconstruction, and (vi) other connections.<\/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":[13561,243138],"msr-publication-type":[193721],"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-313043","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2013-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"1010","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","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":"","msr_publicationurl":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&pg=PA1011&lpg=PA1011&dq=Finite+fields+in+quantum+information+theory&source=bl&ots=HpqvCATPDA&sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&hl=en&sa=X&ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&q=Finite%20fields%20in%20quantum%20information%20theory&f=false","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&pg=PA1011&lpg=PA1011&dq=Finite+fields+in+quantum+information+theory&source=bl&ots=HpqvCATPDA&sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&hl=en&sa=X&ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&q=Finite%20fields%20in%20quantum%20information%20theory&f=false","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&pg=PA1011&lpg=PA1011&dq=Finite+fields+in+quantum+information+theory&source=bl&ots=HpqvCATPDA&sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&hl=en&sa=X&ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&q=Finite%20fields%20in%20quantum%20information%20theory&f=false"}],"msr-author-ordering":[{"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"},{"type":"text","value":"Arne 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