{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T13:42:09Z","timestamp":1648734129913},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> It is proved that the state of maximum entropy, having observed values for the n observables, X<jats:sub>1<\/jats:sub>,\u2026,X<jats:sub>n<\/jats:sub>, is the same state that minimises the matrix of covariances of any n locally unbiased estimators for n parameters for the probability distribution of X<jats:sub>1<\/jats:sub>,\u2026,X<jats:sub>n<\/jats:sub>. We sketch how to get a similar result in quantum theory, in which X<jats:sub>1<\/jats:sub>,\u2026,X<jats:sub>n<\/jats:sub> are (not necessarily commuting) quadratic forms that are bounded relative to a positive self-adjoint operator H such that exp (-\u03b2H) is of trace-class for some positive \u03b2. <\/jats:p>","DOI":"10.1142\/s1230161211000157","type":"journal-article","created":{"date-parts":[[2011,6,22]],"date-time":"2011-06-22T07:49:21Z","timestamp":1308728961000},"page":"223-233","source":"Crossref","is-referenced-by-count":2,"title":["Proof of a Modified Jaynes's Estimation Theory"],"prefix":"10.1142","volume":"18","author":[{"given":"R. F.","family":"Streater","sequence":"first","affiliation":[{"name":"King's College London, Department of Mathematics, Strand, London WC2R 2LS, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","volume-title":"Differential-Geometrical Methods in Statistics","author":"Amari H.-S.","year":"1976"},{"key":"rf2","first-page":"229","volume":"1","author":"Bogoliubov N. N.","journal-title":"Phys. Abh. Soviet Union"},{"key":"rf3","volume-title":"Mathematical Methods of Statistics","author":"Cram\u00e9r H.","year":"1999"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025701000462"},{"key":"rf6","volume-title":"Quantum Detection and Estimation Theory","author":"Helstrom C. W.","year":"1976"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.12.570"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1063\/1.530611"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00211-8"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00739578"},{"key":"rf12","first-page":"1543","volume":"33","author":"Pistone G.","journal-title":"Ann. Stat."},{"key":"rf13","first-page":"81","volume":"37","author":"Rao C. R.","journal-title":"Bull. Calcutter Math. Soc."},{"key":"rf14","first-page":"603","volume":"228","author":"Streater R. F.","journal-title":"Proc. Steklov Institute of Mathematics, Moscow"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1023\/B:OPSY.0000024757.25401.db"},{"key":"rf16","first-page":"357","volume":"11","author":"Streater R. F.","journal-title":"Open Sys. Information Dyn."},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/p576"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161211000157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:39:48Z","timestamp":1565170788000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161211000157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":15,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.1142\/S1230161211000157"],"URL":"https:\/\/doi.org\/10.1142\/s1230161211000157","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6]]}}}