{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T14:07:04Z","timestamp":1768399624887,"version":"3.49.0"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p> We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherence-free subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to non-degenerate codes. We consider several examples, including a detailed analysis of the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes. <\/jats:p>","DOI":"10.1142\/s1230161208000225","type":"journal-article","created":{"date-parts":[[2008,12,29]],"date-time":"2008-12-29T09:49:04Z","timestamp":1230544144000},"page":"329-343","source":"Crossref","is-referenced-by-count":7,"title":["Entropy of a Quantum Error Correction Code"],"prefix":"10.1142","volume":"15","author":[{"given":"David W.","family":"Kribs","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada"},{"name":"Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aron","family":"Pasieka","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karol","family":"\u017byczkowski","sequence":"additional","affiliation":[{"name":"Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiello\u0144ski, ul. Reymonta 4, 30-059 Krak\u00f3w, Poland"},{"name":"Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnik\u00f3w 32\/44, 02\u2013668 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","volume-title":"Quantum Computation and Quantum Information","author":"Nielsen M. A.","year":"2000"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/B0-12-512666-2\/00273-X"},{"key":"rf3","first-page":"382","volume":"6","author":"Kribs D. W.","journal-title":"Quantum Inf. 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