{"id":313043,"date":"2018-11-06T17:12:14","date_gmt":"2018-11-07T01:12:14","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=313043"},"modified":"2018-11-06T17:12:14","modified_gmt":"2018-11-07T01:12:14","slug":"finite-fields-quantum-information-theory","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/finite-fields-quantum-information-theory\/","title":{"rendered":"Finite Fields in Quantum Information Theory"},"content":{"rendered":"<p>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":"<p>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,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"1010","msr_page_range_start":"1010","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2013-01-01","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&#038;pg=PA1011&#038;lpg=PA1011&#038;dq=Finite+fields+in+quantum+information+theory&#038;source=bl&#038;ots=HpqvCATPDA&#038;sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&#038;hl=en&#038;sa=X&#038;ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&#038;q=Finite%20fields%20in%20quantum%20information%20theory&#038;f=false","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561,243138],"msr-publication-type":[193721],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"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&#038;pg=PA1011&#038;lpg=PA1011&#038;dq=Finite+fields+in+quantum+information+theory&#038;source=bl&#038;ots=HpqvCATPDA&#038;sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&#038;hl=en&#038;sa=X&#038;ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&#038;q=Finite%20fields%20in%20quantum%20information%20theory&#038;f=false","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&#038;pg=PA1011&#038;lpg=PA1011&#038;dq=Finite+fields+in+quantum+information+theory&#038;source=bl&#038;ots=HpqvCATPDA&#038;sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&#038;hl=en&#038;sa=X&#038;ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&#038;q=Finite%20fields%20in%20quantum%20information%20theory&#038;f=false","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"https:\/\/books.google.com\/books?id=YADSBQAAQBAJ&#038;pg=PA1011&#038;lpg=PA1011&#038;dq=Finite+fields+in+quantum+information+theory&#038;source=bl&#038;ots=HpqvCATPDA&#038;sig=Y_mpvq8abEEJoxP_SBPlo6LLJqk&#038;hl=en&#038;sa=X&#038;ved=0ahUKEwiMqcLi3YXQAhVM0GMKHVIjAYUQ6AEINzAC#v=onepage&#038;q=Finite%20fields%20in%20quantum%20information%20theory&#038;f=false"}],"msr-author-ordering":[{"type":"user_nicename","value":"martinro","user_id":32823,"rest_url":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=martinro"},{"type":"text","value":"Arne 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