{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T17:08:08Z","timestamp":1769274488187,"version":"3.49.0"},"reference-count":99,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T00:00:00Z","timestamp":1615507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["19-16066S"],"award-info":[{"award-number":["19-16066S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we generalize the notion of Shannon\u2019s entropy power to the R\u00e9nyi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of R\u00e9nyi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the R\u00e9nyi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called \u201ccat states\u201d, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.<\/jats:p>","DOI":"10.3390\/e23030334","type":"journal-article","created":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T11:56:55Z","timestamp":1615550215000},"page":"334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["From R\u00e9nyi Entropy Power to Information Scan of Quantum States"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7940-204X","authenticated-orcid":false,"given":"Petr","family":"Jizba","sequence":"first","affiliation":[{"name":"FNSPE, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7976-3278","authenticated-orcid":false,"given":"Jacob","family":"Dunningham","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK"}]},{"given":"Martin","family":"Prok\u0161","sequence":"additional","affiliation":[{"name":"FNSPE, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha 1, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bennaim, A. 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