{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T07:16:53Z","timestamp":1780816613326,"version":"3.54.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,2,3]],"date-time":"2015-02-03T00:00:00Z","timestamp":1422921600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s11128-015-0935-y","type":"journal-article","created":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T15:46:09Z","timestamp":1422891969000},"page":"1501-1512","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Investigating properties of a family of quantum R\u00e9nyi divergences"],"prefix":"10.1007","volume":"14","author":[{"given":"Simon M.","family":"Lin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Tomamichel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,2,3]]},"reference":[{"key":"935_CR1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"C Shannon","year":"1948","unstructured":"Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379\u2013423 (1948)","journal-title":"Bell Syst. Tech. J."},{"issue":"1","key":"935_CR2","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S Kullback","year":"1951","unstructured":"Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79\u201386 (1951)","journal-title":"Ann. Math. Stat."},{"key":"935_CR3","unstructured":"R\u00e9nyi, A.: On measures of information and entropy. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1: Contributions to the Theory of Statistics, pp. 547\u2013561. University of California Press, Oakland (1961)"},{"issue":"1","key":"935_CR4","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/18.370121","volume":"41","author":"I Csisz\u00e1r","year":"1995","unstructured":"Csisz\u00e1r, I.: Generalized cutoff rates and R\u00e9nyi\u2019s information measures. IEEE Trans. Inf. Theory 41(1), 26\u201334 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"935_CR5","unstructured":"von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932). English Translation, Princeton University Press, Princeton"},{"issue":"2","key":"935_CR6","doi-asserted-by":"crossref","first-page":"59","DOI":"10.2996\/kmj\/1138844604","volume":"14","author":"H Umegaki","year":"1962","unstructured":"Umegaki, H.: Conditional expectations in an operator algebra. IV. Entropy and information. Kodai Math. Semin. Rep. 14(2), 59\u201385 (1962)","journal-title":"Kodai Math. Semin. Rep."},{"key":"935_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-57997-4","volume-title":"Quantum Entropy and Its Use","author":"M Ohya","year":"1993","unstructured":"Ohya, M., Petz, D.: Quantum Entropy and Its Use. Springer, Berlin (1993)"},{"issue":"12","key":"935_CR8","doi-asserted-by":"crossref","first-page":"122203","DOI":"10.1063\/1.4838856","volume":"54","author":"M M\u00fcller-Lennert","year":"2013","unstructured":"M\u00fcller-Lennert, M., Dupuis, F., Szehr, O., Fehr, S., Tomamichel, M.: On quantum R\u00e9nyi entropies: a new generalization and some properties. J. Math. Phys. 54(12), 122203 (2013)","journal-title":"J. Math. Phys."},{"issue":"2","key":"935_CR9","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1007\/s00220-014-2122-x","volume":"331","author":"MM Wilde","year":"2014","unstructured":"Wilde, M.M., Winter, A., Yang, D.: Strong converse for the classical capacity of entanglement-breaking channels. Commun. Math. Phys. 331(2), 593\u2013622 (2014)","journal-title":"Commun. Math. Phys."},{"key":"935_CR10","unstructured":"Mosonyi, M., Ogawa, T.: Quantum hypothesis testing and the operational interpretation of the quantum R\u00e9nyi relative entropies (2013). arXiv:1309.3228"},{"issue":"8","key":"935_CR11","doi-asserted-by":"crossref","first-page":"082206","DOI":"10.1063\/1.4892761","volume":"55","author":"M Tomamichel","year":"2014","unstructured":"Tomamichel, M., Berta, M., Hayashi, M.: Relating different quantum generalizations of the conditional Rnyi entropy. J. Math. Phys. 55(8), 082206 (2014)","journal-title":"J. Math. Phys."},{"key":"935_CR12","unstructured":"Tomamichel, M., Wilde, M.M., Winter, A.: Strong converse bounds for quantum communication (2014). arXiv:1406.2946"},{"key":"935_CR13","unstructured":"Gupta, M.K., Wilde, M.M.: Multiplicativity of completely bounded p-norms implies a strong converse for entanglement-assisted capacity (2013). arXiv:1310.7028"},{"key":"935_CR14","unstructured":"Audenaert, K.M.R., Datta, N.: $$\\alpha $$ \u03b1 \u2013 $$z$$ z -relative R\u00e9nyi entropies (2013). arXiv:1313.7178"},{"issue":"11","key":"935_CR15","doi-asserted-by":"crossref","first-page":"7693","DOI":"10.1109\/TIT.2013.2276628","volume":"59","author":"M Tomamichel","year":"2013","unstructured":"Tomamichel, M., Hayashi, M.: A hierarchy of information quantities for finite block length analysis of quantum tasks. IEEE Trans. Inf. Theory 59(11), 7693\u20137710 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"935_CR16","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1214\/13-AOS1185","volume":"42","author":"K Li","year":"2014","unstructured":"Li, K.: Second-order asymptotics for quantum hypothesis testing. Ann. Stat. 42(1), 171\u2013189 (2014)","journal-title":"Ann. Stat."},{"key":"935_CR17","unstructured":"Tomamichel, M., Tan, V.Y.F.: On the Gaussian approximation for the classical capacity of quantum channels (2013). arXiv:1308.6503"},{"key":"935_CR18","unstructured":"Beigi, S.: Quantum R\u00e9nyi divergence satisfies data processing inequality (2013). arXiv:1306.5920"},{"key":"935_CR19","doi-asserted-by":"crossref","unstructured":"Frank, R.L., Lieb, E.H.: Monotonicity of a relative R\u00e9nyi entropy (2013). arXiv:1306.5358v2","DOI":"10.1063\/1.4838835"},{"issue":"12","key":"935_CR20","doi-asserted-by":"crossref","first-page":"5840","DOI":"10.1109\/TIT.2009.2032797","volume":"55","author":"M Tomamichel","year":"2009","unstructured":"Tomamichel, M., Colbeck, R., Renner, R.: A fully quantum asymptotic equipartition property. IEEE Trans. Inf. Theory 55(12), 5840\u20135847 (2009)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"935_CR21","unstructured":"Tomamichel, M.: A framework for non-asymptotic quantum information theory. Ph.D. thesis, ETH Zurich (2012). arXiv:1203.2142"},{"issue":"4","key":"935_CR22","doi-asserted-by":"crossref","first-page":"045304","DOI":"10.1088\/1751-8113\/47\/4\/045304","volume":"47","author":"N Datta","year":"2014","unstructured":"Datta, N., Leditzky, F.: A limit of the quantum R\u00e9nyi divergence. J. Phys. A: Math. Theor. 47(4), 045304 (2014)","journal-title":"J. Phys. A: Math. Theor."},{"key":"935_CR23","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF01045887","volume":"19","author":"H Araki","year":"1990","unstructured":"Araki, H.: On an inequality of lieb and thirring. Lett. Math. Phys. 19, 167\u2013170 (1990)","journal-title":"Lett. Math. Phys."},{"key":"935_CR24","first-page":"269","volume-title":"Stud. Math. Phys.","author":"EH Lieb","year":"1976","unstructured":"Lieb, E.H., Thirring, W.E.: Inequalities for the moments of the eigenvalues of the Schr\u00f6dinger Hamiltonian and their relation to Sobolev inequalities. In: Lieb, E.H., Simon, B., Wrightman, A.S. (eds.) Stud. Math. Phys., pp. 269\u2013303. Princeton Press, Princeton (1976)"},{"key":"935_CR25","unstructured":"Mosonyi, M., Ogawa, T.: The strong converse exponent of quantum hypothesis testing for correlated quantum states (2014). arXiv:1407.3567"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-015-0935-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-015-0935-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-015-0935-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T12:53:08Z","timestamp":1566305588000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-015-0935-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,3]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["935"],"URL":"https:\/\/doi.org\/10.1007\/s11128-015-0935-y","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,3]]}}}