{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T10:02:25Z","timestamp":1767866545411,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2015,2,20]],"date-time":"2015-02-20T00:00:00Z","timestamp":1424390400000},"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":[[2015,6]]},"DOI":"10.1007\/s11128-015-0949-5","type":"journal-article","created":{"date-parts":[[2015,2,19]],"date-time":"2015-02-19T09:02:07Z","timestamp":1424336527000},"page":"2227-2238","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Uncertainty relations based on mutually unbiased measurements"],"prefix":"10.1007","volume":"14","author":[{"given":"Bin","family":"Chen","sequence":"first","affiliation":[]},{"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,20]]},"reference":[{"key":"949_CR1","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1103\/PhysRev.34.163","volume":"34","author":"HP Robertson","year":"1929","unstructured":"Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163\u2013164 (1929)","journal-title":"Phys. Rev."},{"key":"949_CR2","unstructured":"Tsallis, C. et al.: Nonextensive Statistical Mechanics and Its Applications. Abe, S., Okamoto, Y. (eds.). Springer-Verlag, Heidelberg (2001)"},{"key":"949_CR3","doi-asserted-by":"crossref","first-page":"51402","DOI":"10.1103\/PhysRevA.67.051402","volume":"67","author":"E Lutz","year":"2003","unstructured":"Lutz, E.: Anomalous diffusion and Tsallis statistics in an optical lattice. Phys. Rev. A 67, 51402 (2003). (R)","journal-title":"Phys. Rev. A"},{"key":"949_CR4","doi-asserted-by":"crossref","first-page":"110601","DOI":"10.1103\/PhysRevLett.96.110601","volume":"96","author":"P Douglas","year":"2006","unstructured":"Douglas, P., Bergamini, S., Renzoni, F.: Tunable Tsallis distributions in dissipative optical lattices. Phys. Rev. Lett. 96, 110601 (2006)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR5","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.physa.2005.06.065","volume":"356","author":"LF Burlaga","year":"2005","unstructured":"Burlaga, L.F., Vinas, A.F.: Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere. Phys. A 356, 375\u2013384 (2005)","journal-title":"Phys. A"},{"key":"949_CR6","doi-asserted-by":"crossref","first-page":"055003","DOI":"10.1103\/PhysRevLett.100.055003","volume":"100","author":"B Liu","year":"2008","unstructured":"Liu, B., Goree, J.: Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma. Phys. Rev. Lett. 100, 055003 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR7","doi-asserted-by":"crossref","first-page":"097202","DOI":"10.1103\/PhysRevLett.102.097202","volume":"102","author":"R Pickup","year":"2009","unstructured":"Pickup, R., Cywinski, R., Pappas, C., Farago, B., Fouquet, P.: Generalized spin-glass relaxation. Phys. Rev. Lett. 102, 097202 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR8","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1103\/PhysRevLett.50.631","volume":"50","author":"D Deutsch","year":"1983","unstructured":"Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631\u2013633 (1983)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR9","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1103\/PhysRevLett.60.1103","volume":"60","author":"H Maassen","year":"1988","unstructured":"Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103\u20131106 (1988)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR10","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0003-4916(89)90322-9","volume":"191","author":"WK Wootters","year":"1989","unstructured":"Wootters, W.K., Fields, B.D.: Optimal state-determination by mutually unbiased measurements. Ann. Phys. 191, 363\u2013381 (1989). (N.Y.)","journal-title":"Ann. Phys."},{"key":"949_CR11","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1142\/S0219749910006502","volume":"08","author":"T Durt","year":"2010","unstructured":"Durt, T., Englert, B.-G., Bengtsson, I., \u017byczkowski, K.: On mutually unbiased bases. Int. J. Quantum Inf. 08, 535 (2010)","journal-title":"Int. J. Quantum Inf."},{"key":"949_CR12","doi-asserted-by":"crossref","first-page":"L363","DOI":"10.1088\/0305-4470\/25\/7\/014","volume":"25","author":"ID Ivanovi\u0107","year":"1992","unstructured":"Ivanovi\u0107, I.D.: An inequality for the sum of entropies of unbiased quantum measurements. J. Phys. A 25, L363\u2013L364 (1992)","journal-title":"J. Phys. A"},{"key":"949_CR13","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0375-9601(93)90269-6","volume":"173","author":"J S\u00e1nchez","year":"1993","unstructured":"S\u00e1nchez, J.: Entropic uncertainty and certainty relations for complementary observables. Phys. Lett. A 173, 233\u2013239 (1993)","journal-title":"Phys. Lett. A"},{"key":"949_CR14","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0375-9601(95)00219-S","volume":"201","author":"J S\u00e1nchez-Ruiz","year":"1995","unstructured":"S\u00e1nchez-Ruiz, J.: Improved bounds in the entropic uncertainty and certainty relations for complementary observables. Phys. Lett. A 201, 125\u2013131 (1995)","journal-title":"Phys. Lett. A"},{"key":"949_CR15","doi-asserted-by":"crossref","first-page":"022104","DOI":"10.1103\/PhysRevA.79.022104","volume":"79","author":"S Wu","year":"2009","unstructured":"Wu, S., Yu, S., M\u00f8lmer, K.: Entropic uncertainty relation for mutually unbiased bases. Phys. Rev. A 79, 022104 (2009)","journal-title":"Phys. Rev. A"},{"key":"949_CR16","doi-asserted-by":"crossref","first-page":"025009","DOI":"10.1088\/1367-2630\/12\/2\/025009","volume":"12","author":"S Wehner","year":"2010","unstructured":"Wehner, S., Winter, A.: Entropic uncertainty relations\u2014a survey. New J. Phys. 12, 025009 (2010)","journal-title":"New J. Phys."},{"key":"949_CR17","doi-asserted-by":"crossref","first-page":"053038","DOI":"10.1088\/1367-2630\/16\/5\/053038","volume":"16","author":"A Kalev","year":"2014","unstructured":"Kalev, A., Gour, G.: Mutually unbiased measurements in finite dimensions. New J. Phys. 16, 053038 (2014)","journal-title":"New J. Phys."},{"key":"949_CR18","doi-asserted-by":"crossref","first-page":"042203","DOI":"10.1063\/1.3374022","volume":"51","author":"AJ Scott","year":"2010","unstructured":"Scott, A.J., Grassl, M.: Symmetric informationally complete positive-operator-valued measures: a new computer study. J. Math. Phys. 51, 042203 (2010)","journal-title":"J. Math. Phys."},{"key":"949_CR19","doi-asserted-by":"crossref","first-page":"335302","DOI":"10.1088\/1751-8113\/47\/33\/335302","volume":"47","author":"G Gour","year":"2014","unstructured":"Gour, G., Kalev, A.: Construction of all general symmetric informationally complete measurements. J. Phys. A Math. Theor. 47, 335302 (2014)","journal-title":"J. Phys. A Math. Theor."},{"key":"949_CR20","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1140\/epjd\/e2013-40453-2","volume":"67","author":"AE Rastegin","year":"2013","unstructured":"Rastegin, A.E.: Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies. Eur. Phys. J. D 67, 269 (2013)","journal-title":"Eur. Phys. J. D"},{"key":"949_CR21","doi-asserted-by":"crossref","first-page":"085101","DOI":"10.1088\/0031-8949\/89\/8\/085101","volume":"89","author":"AE Rastegin","year":"2014","unstructured":"Rastegin, A.E.: Notes on general SIC-POVMs. Phys. Scr. 89, 085101 (2014)","journal-title":"Phys. Scr."},{"key":"949_CR22","doi-asserted-by":"crossref","first-page":"272002","DOI":"10.1088\/1751-8113\/46\/27\/272002","volume":"46","author":"Z Pucha\u0142a","year":"2013","unstructured":"Pucha\u0142a, Z., Rudnicki, \u0141., \u017byczkowski, K.: Majorization entropic uncertainty relations. J. Phys. A Math. Theor. 46, 272002 (2013)","journal-title":"J. Phys. A Math. Theor."},{"key":"949_CR23","doi-asserted-by":"crossref","first-page":"052115","DOI":"10.1103\/PhysRevA.89.052115","volume":"89","author":"\u0141 Rudnicki","year":"2014","unstructured":"Rudnicki, \u0141., Pucha\u0142a, Z., \u017byczkowski, K.: Strong majorization entropic uncertainty relations. Phys. Rev. A 89, 052115 (2014)","journal-title":"Phys. Rev. A"},{"key":"949_CR24","doi-asserted-by":"crossref","first-page":"230401","DOI":"10.1103\/PhysRevLett.111.230401","volume":"111","author":"S Friedland","year":"2013","unstructured":"Friedland, S., Gheorghiu, V., Gour, G.: Universal uncertainty relations. Phys. Rev. Lett. 111, 230401 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"949_CR25","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.1109\/18.959272","volume":"47","author":"P Harremo\u00ebs","year":"2001","unstructured":"Harremo\u00ebs, P., Tops\u00f8e, F.: Inequalities between entropy and index of coincidence derived from information diagrams. IEEE Trans. Inf. Theory 47, 2944\u20132960 (2001)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"949_CR26","unstructured":"R\u00e9nyi, A.: In Proceedings of 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. I, pp. 547\u2013561. University of California Press, Berkeley (1961)"},{"key":"949_CR27","doi-asserted-by":"crossref","first-page":"022319","DOI":"10.1103\/PhysRevA.75.022319","volume":"75","author":"MA Ballester","year":"2007","unstructured":"Ballester, M.A., Wehner, S.: Entropic uncertainty relations and locking: Tight bounds for mutually unbiased bases. Phys. Rev. A 75, 022319 (2007)","journal-title":"Phys. Rev. A"},{"key":"949_CR28","doi-asserted-by":"crossref","first-page":"042315","DOI":"10.1103\/PhysRevA.86.042315","volume":"86","author":"HYN Ng","year":"2012","unstructured":"Ng, H.Y.N., Berta, M., Wehner, S.: Min-entropy uncertainty relation for finite-size cryptography. Phys. Rev. A 86, 042315 (2012)","journal-title":"Phys. Rev. A"},{"key":"949_CR29","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","volume":"52","author":"C Tsallis","year":"1988","unstructured":"Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479\u2013487 (1988)","journal-title":"J. Stat. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-015-0949-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-015-0949-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-015-0949-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T07:39:20Z","timestamp":1559374760000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-015-0949-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,20]]},"references-count":29,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["949"],"URL":"https:\/\/doi.org\/10.1007\/s11128-015-0949-5","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,20]]}}}