{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T12:51:57Z","timestamp":1773924717660,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s11128-021-03238-2","type":"journal-article","created":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T06:03:40Z","timestamp":1632204220000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An efficient superpostional quantum Johnson\u2013Lindenstrauss lemma via unitary t-designs"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0193-8562","authenticated-orcid":false,"given":"Pranab","family":"Sen","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,21]]},"reference":[{"key":"3238_CR1","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1137\/060673096","volume":"39","author":"N Ailon","year":"2009","unstructured":"Ailon, N., Chazelle, B.: The fast Johnson\u2013Lindenstrauss transform and approximate nearest neighbors. SIAM J. Comput. 39, 302\u2013322 (2009)","journal-title":"SIAM J. Comput."},{"key":"3238_CR2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801334","volume-title":"An Introduction to Random Matrices","author":"G Anderson","year":"2009","unstructured":"Anderson, G., Guionnet, A., Zeitouni, O.: An Introduction to Random Matrices. Cambridge University Press, Cambridge (2009)"},{"key":"3238_CR3","doi-asserted-by":"crossref","unstructured":"Bellare, M., Rompel, J.: Randomness-efficient oblivious sampling. In: 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 276\u2013287 (1994)","DOI":"10.1109\/SFCS.1994.365687"},{"key":"3238_CR4","doi-asserted-by":"publisher","first-page":"47","DOI":"10.4086\/toc.2010.v006a003","volume":"6","author":"A Ben-Aroya","year":"2010","unstructured":"Ben-Aroya, A., Schwartz, O., Ta-Shma, A.: Quantum expanders: motivation and construction. Theory Comput. 6, 47\u201379 (2010)","journal-title":"Theory Comput."},{"issue":"15","key":"3238_CR5","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1016\/j.laa.2018.11.012","volume":"563","author":"A Bluhm","year":"2019","unstructured":"Bluhm, A., Fran\u00e7a, D.: Dimensionality reduction of SDPs through sketching. Linear Algebra Appl. 563(15), 461\u2013475 (2019)","journal-title":"Linear Algebra Appl."},{"key":"3238_CR6","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s00220-016-2706-8","volume":"346","author":"F Brand\u00e3o","year":"2016","unstructured":"Brand\u00e3o, F., Harrow, A., Horodecki, M.: Local random quantum circuits are approximate polynomial-designs. Commun. Math. Phys. 346, 397\u2013434 (2016)","journal-title":"Commun. Math. Phys."},{"key":"3238_CR7","doi-asserted-by":"publisher","first-page":"167902:1","DOI":"10.1103\/PhysRevLett.87.167902","volume":"87","author":"H Buhrman","year":"2001","unstructured":"Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87, 167902:1-167902:4 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"3238_CR8","doi-asserted-by":"publisher","first-page":"1723","DOI":"10.1137\/S0097539702405292","volume":"31","author":"H Buhrman","year":"2002","unstructured":"Buhrman, H., Miltersen, P., Radhakrishnan, J., Venkatesh, S.: Are bitvectors optimal? SIAM J. Comput. 31, 1723\u20131744 (2002)","journal-title":"SIAM J. Comput."},{"key":"3238_CR9","doi-asserted-by":"crossref","unstructured":"Capalbo, M., Reingold, O., Vadhan, S., Wigderson, A.: Randomness conductors and constant-degree lossless expanders. In: 34th Annual ACM Symposium on Theory of Computing (STOC), pp. 659\u2013668 (2002)","DOI":"10.1145\/509907.510003"},{"key":"3238_CR10","unstructured":"Cleve, R., H\u00f8yer, P., Toner, B., Watrous, J.: Consequences and limits of nonlocal strategies. In: 19th Annual IEEE Conference on Computational Complexity (CCC), pp. 236\u2013249 (2004)"},{"key":"3238_CR11","unstructured":"Coppersmith, D.: An approximate Fourier transform useful in quantum factoring. IBM Research Report RC 19642 (1994). arXiv:1709.07268"},{"issue":"44","key":"3238_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2518131","volume":"60","author":"O Fawzi","year":"2013","unstructured":"Fawzi, O., Hayden, P., Sen, P.: From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking. J. ACM 60(44), 1\u201361 (2013). https:\/\/doi.org\/10.1145\/2518131","journal-title":"J. ACM"},{"key":"3238_CR13","doi-asserted-by":"crossref","unstructured":"Gavinsky, D., Kempe, J., de Wolf, R.: Strengths and weaknesses of quantum fingerprinting. In: 21st Annual IEEE Conference on Computational Complexity (CCC), pp. 288\u2013298 (2006)","DOI":"10.1109\/CCC.2006.39"},{"key":"3238_CR14","doi-asserted-by":"crossref","unstructured":"Harrow, A., Montanaro, A., Short, A.: Limitations on quantum dimensionality reduction. In: International Colloquium on Automata, Languages and Programming (ICALP), pp. 86\u201397 (2011). arXiv:1012.2262","DOI":"10.1007\/978-3-642-22006-7_8"},{"issue":"3","key":"3238_CR15","first-page":"336","volume":"9","author":"M Hastings","year":"2009","unstructured":"Hastings, M., Harrow, A.: Classical and quantum tensor product expanders. Quantum Inf. Comput. 9(3), 336\u2013360 (2009)","journal-title":"Quantum Inf. Comput."},{"key":"3238_CR16","doi-asserted-by":"publisher","first-page":"33:1","DOI":"10.1145\/1568318.1568323","volume":"56","author":"R Jain","year":"2009","unstructured":"Jain, R., Radhakrishnan, J., Sen, P.: A property of quantum relative entropy with an application to privacy in quantum communication. J. ACM 56, 33:1-33:32 (2009)","journal-title":"J. ACM"},{"key":"3238_CR17","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1090\/conm\/026\/737400","volume":"26","author":"W Johnson","year":"1984","unstructured":"Johnson, W., Lindenstrauss, J.: Extensions of Lipschitz mappings into a Hilbert space. Contemp. Math. 26, 189\u2013206 (1984)","journal-title":"Contemp. Math."},{"key":"3238_CR18","doi-asserted-by":"publisher","first-page":"3289","DOI":"10.1098\/rspa.2009.0232","volume":"465","author":"R Low","year":"2009","unstructured":"Low, R.: Large deviation bounds for $$k$$-designs. Proc. R. Soc. A Math. Phys. Eng. Sci. 465, 3289\u20133308 (2009). https:\/\/doi.org\/10.1098\/rspa.2009.0232","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"issue":"1","key":"3238_CR19","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1142\/S0219749904000109","volume":"2","author":"M Mosca","year":"2004","unstructured":"Mosca, M., Zalka, C.: Exact quantum Fourier transforms and discrete logarithm algorithms. Int. J. Quantum Inf. 2(1), 91\u2013100 (2004)","journal-title":"Int. J. Quantum Inf."},{"issue":"2","key":"3238_CR20","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/0020-0190(91)90157-D","volume":"39","author":"I Newman","year":"1991","unstructured":"Newman, I.: Private vs. common random bits in communication complexity. Inf. Process. Lett. 39(2), 67\u201371 (1991)","journal-title":"Inf. Process. Lett."},{"key":"3238_CR21","unstructured":"Sen, P.: Efficient quantum tensor product expanders and unitary $$t$$-designs via the zigzag product (2018). arXiv:1808.10521"},{"key":"3238_CR22","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"P Shor","year":"1997","unstructured":"Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484\u20131509 (1997)","journal-title":"SIAM J. Comput."},{"issue":"5","key":"3238_CR23","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/S0020-0190(02)00206-5","volume":"83","author":"A Ta-Shma","year":"2002","unstructured":"Ta-Shma, A.: Storing information with extractors. Inf. Process. Lett. 83(5), 267\u2013274 (2002)","journal-title":"Inf. Process. Lett."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03238-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03238-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03238-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T16:34:34Z","timestamp":1725813274000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03238-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":23,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["3238"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03238-2","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9]]},"assertion":[{"value":"8 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declares that he has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"312"}}