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It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on R\u00e9nyi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.<\/jats:p>","DOI":"10.22331\/q-2021-09-14-541","type":"journal-article","created":{"date-parts":[[2021,9,14]],"date-time":"2021-09-14T17:55:20Z","timestamp":1631642120000},"page":"541","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":18,"title":["Computable R\u00e9nyi mutual information: Area laws and correlations"],"prefix":"10.22331","volume":"5","author":[{"given":"Samuel O.","family":"Scalet","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 M\u00fcnchen, Germany"}]},{"given":"\u00c1lvaro M.","family":"Alhambra","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 M\u00fcnchen, Germany"}]},{"given":"Georgios","family":"Styliaris","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 M\u00fcnchen, Germany"}]},{"given":"J. Ignacio","family":"Cirac","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, D-85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 M\u00fcnchen, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2021,9,14]]},"reference":[{"key":"0","unstructured":"J. Eisert, arXiv:1308.3318 [quant-ph]."},{"key":"1","unstructured":"I. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, arXiv:2011.12127 [quant-ph]."},{"key":"2","doi-asserted-by":"publisher","unstructured":"F. Verstraete and J. I. Cirac, Phys. Rev. B 73, 094423 (2006).","DOI":"10.1103\/PhysRevB.73.094423"},{"key":"3","doi-asserted-by":"publisher","unstructured":"M. B. Hastings, J. Stat. Mech. 2007, P08024 (2007).","DOI":"10.1088\/1742-5468\/2007\/08\/p08024"},{"key":"4","doi-asserted-by":"publisher","unstructured":"M. B. Hastings, Phys. Rev. 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