{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T21:41:38Z","timestamp":1791409298466,"version":"4.3.3"},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540741428","type":"print"},{"value":"9783540741435","type":"electronic"}],"license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-74143-5_20","type":"book-chapter","created":{"date-parts":[[2007,8,9]],"date-time":"2007-08-09T09:51:33Z","timestamp":1186653093000},"page":"360-378","source":"Crossref","is-referenced-by-count":57,"title":["A Tight High-Order Entropic Quantum Uncertainty Relation with Applications"],"prefix":"10.1007","author":[{"given":"Ivan B.","family":"Damg\u00e5rd","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Serge","family":"Fehr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renato","family":"Renner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Louis","family":"Salvail","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Schaffner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"20_CR1","series-title":"Series in Discrete Mathematics and Optimization","doi-asserted-by":"crossref","DOI":"10.1002\/0471722154","volume-title":"The Probabilistic Method","author":"N. Alon","year":"2000","unstructured":"Alon, N., Spencer, J.: The Probabilistic Method, 2nd edn. Series in Discrete Mathematics and Optimization. Wiley, Chichester (2000)","edition":"2"},{"key":"20_CR2","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2748\/tmj\/1178243286","volume":"19","author":"K. Azuma","year":"1967","unstructured":"Azuma, K.: Weighted sums of certain dependent random variables. T\u00f4hoku Mathematical Journal\u00a019, 357\u2013367 (1967)","journal-title":"T\u00f4hoku Mathematical Journal"},{"key":"20_CR3","first-page":"175","volume-title":"Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing","author":"C.H. Bennett","year":"1984","unstructured":"Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, pp. 175\u2013179. IEEE Computer Society Press, Los Alamitos (1984)"},{"key":"20_CR4","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1109\/18.476316","volume":"41","author":"C.H. Bennett","year":"1995","unstructured":"Bennett, C.H., Brassard, G., Cr\u00e9peau, C., Maurer, U.M.: Generalized privacy amplification. IEEE Transactions on Information Theory\u00a041, 1915\u20131923 (1995)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"20_CR5","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1137\/0217014","volume":"17","author":"C.H. Bennett","year":"1988","unstructured":"Bennett, C.H., Brassard, G., Robert, J.-M.: Privacy amplification by public discussion. SIAM J. Comput.\u00a017(2), 210\u2013229 (1988)","journal-title":"SIAM J. Comput."},{"key":"20_CR6","doi-asserted-by":"publisher","first-page":"52101","DOI":"10.1103\/PhysRevA.74.052101","volume":"74","author":"I. Bialynicki-Birula","year":"2006","unstructured":"Bialynicki-Birula, I.: Formulation of the uncertainty relations in terms of the R\u00e9nyi entropies. Physical Review A\u00a074, 52101 (2006)","journal-title":"Physical Review A"},{"key":"20_CR7","doi-asserted-by":"crossref","unstructured":"Bialynicki-Birula, I., Mycielski, J.: Uncertainty relations for information entropy. Communications in Mathematical Physics\u00a0129(44) (1975)","DOI":"10.1007\/BF01608825"},{"key":"20_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/3-540-69053-0_14","volume-title":"Advances in Cryptology - EUROCRYPT 1997","author":"C. Cachin","year":"1997","unstructured":"Cachin, C.: Smooth entropy and R\u00e9nyi entropy. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol.\u00a01233, pp. 193\u2013208. Springer, Heidelberg (1997)"},{"key":"20_CR9","first-page":"106","volume-title":"STOC","author":"J.L. Carter","year":"1977","unstructured":"Carter, J.L., Wegman, M.N.: Universal classes of hash functions. In: STOC. 9th Annual ACM Symposium on Theory of Computing, pp. 106\u2013112. ACM Press, New York (1977)"},{"key":"20_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1007\/11761679_32","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"C. Cr\u00e9peau","year":"2006","unstructured":"Cr\u00e9peau, C., Savvides, G., Schaffner, C., Wullschleger, J.: Information-theoretic conditions for two-party secure function evaluation. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 538\u2013554. Springer, Heidelberg (2006)"},{"issue":"3","key":"20_CR11","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","volume":"24","author":"I. Csisz\u00e1r","year":"1978","unstructured":"Csisz\u00e1r, I., K\u00f6rner, J.: Broadcast channels with confidential messages. IEEE Transactions on Information Theory\u00a024(3), 339\u2013348 (1978)","journal-title":"IEEE Transactions on Information Theory"},{"key":"20_CR12","unstructured":"Damg\u00e5rd, I.B., Fehr, S., Renner, R., Salvail, L., Schaffner, C.: A tight high-order entropic quantum uncertainty relation with applications (2007), Available at \n                    \n                      http:\/\/arxiv.org\/abs\/quant-ph\/0612014"},{"key":"20_CR13","first-page":"449","volume-title":"FOCS","author":"I.B. Damg\u00e5rd","year":"2005","unstructured":"Damg\u00e5rd, I.B., Fehr, S., Salvail, L., Schaffner, C.: Cryptography in the bounded quantum-storage model. In: FOCS. 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 449\u2013458. IEEE Computer Society Press, Los Alamitos (2005)"},{"key":"20_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/11818175_26","volume-title":"Advances in Cryptology - CRYPTO 2006","author":"I.B. Damg\u00e5rd","year":"2006","unstructured":"Damg\u00e5rd, I.B., Fehr, S., Salvail, L., Schaffner, C.: Oblivious transfer and linear functions. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol.\u00a04117, pp. 427\u2013444. Springer, Heidelberg (2006)"},{"key":"20_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/978-3-540-24676-3_6","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"I.B. Damg\u00e5rd","year":"2004","unstructured":"Damg\u00e5rd, I.B., Pedersen, T.B., Salvail, L.: On the key-uncertainty of quantum ciphers and the computational security of one-way quantum transmission. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 91\u2013108. Springer, Heidelberg (2004)"},{"issue":"9","key":"20_CR16","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1103\/PhysRevLett.50.631","volume":"50","author":"D. Deutsch","year":"1983","unstructured":"Deutsch, D.: Uncertainty in quantum measurements. Physical Review Letters\u00a050(9), 631\u2013633 (1983)","journal-title":"Physical Review Letters"},{"key":"20_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/3-540-45539-6_21","volume-title":"Advances in Cryptology - EUROCRYPT 2000","author":"P. Dumais","year":"2000","unstructured":"Dumais, P., Mayers, D., Salvail, L.: Perfectly concealing quantum bit commitment from any quantum one-way permutation. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol.\u00a01807, pp. 300\u2013315. Springer, Heidelberg (2000)"},{"key":"20_CR18","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1103\/PhysRevA.56.1163","volume":"56","author":"C.A. Fuchs","year":"1997","unstructured":"Fuchs, C.A., Gisin, N., Griffiths, R.B., Niu, C.-S., Peres, A.: Optimal eavesdropping in quantum cryptography. Physical Review A\u00a056, 1163\u20131172 (1997)","journal-title":"Physical Review A"},{"key":"20_CR19","volume-title":"Microphysical Reality and Quantum Description","author":"J. Hilgevood","year":"1988","unstructured":"Hilgevood, J., Uffink, J.: The mathematical expression of the uncertainty principle. In: Microphysical Reality and Quantum Description, Kluwer Academic Publishers, Dordrecht (1988)"},{"key":"20_CR20","first-page":"12","volume-title":"STOC","author":"R. Impagliazzo","year":"1989","unstructured":"Impagliazzo, R., Levin, L.A., Luby, M.: Pseudo-random generation from one-way functions. In: STOC. 21st Annual ACM Symposium on Theory of Computing, pp. 12\u201324. ACM Press, New York (1989)"},{"issue":"10","key":"20_CR21","doi-asserted-by":"publisher","first-page":"3070","DOI":"10.1103\/PhysRevD.35.3070","volume":"35","author":"K. Kraus","year":"1987","unstructured":"Kraus, K.: Complementary observables and uncertainty relations. Physical Review D\u00a035(10), 3070\u20133075 (1987)","journal-title":"Physical Review D"},{"issue":"7","key":"20_CR22","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.1088\/0305-4470\/23\/7\/013","volume":"23","author":"U. Larsen","year":"1990","unstructured":"Larsen, U.: Superspace geometry: the exact uncertainty relationship between complementary aspects. Journal of Physics A: Mathematical and General\u00a023(7), 1041\u20131061 (1990)","journal-title":"Journal of Physics A: Mathematical and General"},{"key":"20_CR23","doi-asserted-by":"publisher","first-page":"52304","DOI":"10.1103\/PhysRevA.61.052304","volume":"61","author":"N. L\u00fctkenhaus","year":"2000","unstructured":"L\u00fctkenhaus, N.: Security against individual attacks for realistic quantum key distribution. Physical Review A\u00a061, 52304 (2000)","journal-title":"Physical Review A"},{"issue":"12","key":"20_CR24","doi-asserted-by":"publisher","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. Physical Review Letters\u00a060(12), 1103\u20131106 (1988)","journal-title":"Physical Review Letters"},{"key":"20_CR25","unstructured":"Renner, R.: Security of Quantum Key Distribution. PhD thesis, ETH Z\u00fcrich (2005), \n                    \n                      http:\/\/arxiv.org\/abs\/quant-ph\/0512258"},{"key":"20_CR26","doi-asserted-by":"crossref","unstructured":"Renner, R., Gisin, N., Kraus, B.: An information-theoretic security proof for QKD protocols. Phys. Rev. A.\u00a072(012332) (2005)","DOI":"10.1103\/PhysRevA.72.012332"},{"key":"20_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/978-3-540-30576-7_22","volume-title":"Theory of Cryptography","author":"R. Renner","year":"2005","unstructured":"Renner, R., K\u00f6nig, R.: Universally composable privacy amplification against quantum adversaries. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 407\u2013425. Springer, Heidelberg (2005)"},{"key":"20_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/11593447_11","volume-title":"Advances in Cryptology - ASIACRYPT 2005","author":"R. Renner","year":"2005","unstructured":"Renner, R., Wolf, S.: Simple and tight bounds for information reconciliation and privacy amplification. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol.\u00a03788, pp. 199\u2013216. Springer, Heidelberg (2005)"},{"issue":"3","key":"20_CR29","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0375-9601(93)90269-6","volume":"173","author":"J. S\u00e1nchez-Ruiz","year":"1993","unstructured":"S\u00e1nchez-Ruiz, J.: Entropic uncertainty and certainty relations for complementary observables. Physics Letters A\u00a0173(3), 233\u2013239 (1993)","journal-title":"Physics Letters A"},{"issue":"2\u20133","key":"20_CR30","doi-asserted-by":"publisher","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. Physics Letters A\u00a0201(2\u20133), 125\u2013131 (1995)","journal-title":"Physics Letters A"},{"key":"20_CR31","first-page":"175","volume-title":"FOCS","author":"M.N. Wegman","year":"1979","unstructured":"Wegman, M.N., Carter, J.L.: New classes and applications of hash functions. In: FOCS. 20th Annual IEEE Symposium on Foundations of Computer Science, pp. 175\u2013182. IEEE Computer Society Press, Los Alamitos (1979)"},{"issue":"1","key":"20_CR32","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1145\/1008908.1008920","volume":"15","author":"S. Wiesner","year":"1970","unstructured":"Wiesner, S.: Conjugate coding. SIGACT News\u00a015(1), 78\u201388 (1970)","journal-title":"SIGACT News"},{"key":"20_CR33","series-title":"Lecture Notes in Computer Science","volume-title":"Advances in Cryptology\u2014EUROCRYPT\u00a0\u201907","author":"J. Wullschleger","year":"2007","unstructured":"Wullschleger, J.: Oblivious-Transfer amplification. In: Advances in Cryptology\u2014EUROCRYPT\u00a0\u201907. LNCS, Springer, Heidelberg (2007)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - CRYPTO 2007"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-74143-5_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T10:04:37Z","timestamp":1558260277000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-74143-5_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540741428","9783540741435"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-74143-5_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}