{"id":184096,"date":"2005-05-24T00:00:00","date_gmt":"2009-10-31T13:22:25","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/entanglement-entropy-in-extended-systems\/"},"modified":"2016-09-09T09:50:54","modified_gmt":"2016-09-09T16:50:54","slug":"entanglement-entropy-in-extended-systems","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/entanglement-entropy-in-extended-systems\/","title":{"rendered":"Entanglement Entropy in Extended Systems"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Consider a quantum system with short-ranged interactions in some domain D, in its ground state. Alice can measure only observables localized within a subdomain A, and Bob can measure only those in the complement. One measure of the degree of quantum entanglement between Alice&#8217;s and Bob&#8217;s measurements is the von Neumann entropy <i>S<sub>A<\/sub>=-Tr &rho;<sub>Alog<\/sub> &rho;<sub>A<\/sub><\/i> corresponding to A&#8217;s reduced density matrix <i>&rho;<sub>A<\/sub><\/i>. In this talk I review path integral methods for computing this and discuss how the form of the results depends on (a) the geometry and (b) whether the system is at a quantum critical point.  They also illustrate the connection between this zero-temperature entropy and the usual Gibbs-Boltzmann entropy.  Results are also presented for the time-dependence of <i>S<sub>A<\/sub><\/i> starting from a general unentangled state. This work was carried out with P. Calabrese.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider a quantum system with short-ranged interactions in some domain D, in its ground state. Alice can measure only observables localized within a subdomain A, and Bob can measure only those in the complement. One measure of the degree of quantum entanglement between Alice&#8217;s and Bob&#8217;s measurements is the von Neumann entropy SA=-Tr &rho;Alog &rho;A [&hellip;]<\/p>\n","protected":false},"featured_media":195319,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-184096","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/k2K4nwCaFnE","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184096\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195319"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=184096"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=184096"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=184096"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=184096"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=184096"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=184096"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=184096"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=184096"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=184096"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=184096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}