{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T00:45:21Z","timestamp":1773967521034,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61531003"],"award-info":[{"award-number":["61531003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61427813"],"award-info":[{"award-number":["61427813"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s11128-020-02936-7","type":"journal-article","created":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T10:06:10Z","timestamp":1610013970000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Finite-size analysis of continuous variable source-independent quantum random number generation"],"prefix":"10.1007","volume":"20","author":[{"given":"Junyu","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6162-4066","authenticated-orcid":false,"given":"Yichen","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Ziyong","family":"Zheng","sequence":"additional","affiliation":[]},{"given":"Ziyang","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Bingjie","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Song","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"issue":"1","key":"2936_CR1","doi-asserted-by":"publisher","first-page":"015004","DOI":"10.1103\/RevModPhys.89.015004","volume":"89","author":"M Herrero-Collantes","year":"2017","unstructured":"Herrero-Collantes, M., Garcia-Escartin, J.C.: Quantum random number generators. Rev. Mod. Phys. 89(1), 015004 (2017)","journal-title":"Rev. Mod. Phys."},{"key":"2936_CR2","doi-asserted-by":"publisher","first-page":"16021","DOI":"10.1038\/npjqi.2016.21","volume":"2","author":"X Ma","year":"2016","unstructured":"Ma, X., Yuan, X., Cao, Z., Qi, B., Zhang, Z.: Quantum random number generation npj. Quantum Inf. 2, 16021 (2016)","journal-title":"Quantum Inf."},{"issue":"4","key":"2936_CR3","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1364\/OL.43.000631","volume":"43","author":"L Nguyen","year":"2018","unstructured":"Nguyen, L., Rehain, P., Sua, Y.M., Huang, Y.: Programmable quantum random number generator without postprocessing. Opt. Lett. 43(4), 631\u2013634 (2018)","journal-title":"Opt. Lett."},{"issue":"2","key":"2936_CR4","first-page":"1","volume":"7","author":"J Wang","year":"2015","unstructured":"Wang, J., Xie, T., Zhang, H., Yang, D., Xie, C., Wang, J.: A bias-free quantum random number generation using photon arrival time selectively. IEEE Photonics J. 7(2), 1\u20138 (2015)","journal-title":"IEEE Photonics J."},{"issue":"7","key":"2936_CR5","doi-asserted-by":"publisher","first-page":"073113","DOI":"10.1063\/1.4927320","volume":"86","author":"Q Yan","year":"2015","unstructured":"Yan, Q., Zhao, B., Hua, Z., Liao, Q., Yang, H.: High-speed quantum-random number generation by continuous measurement of arrival time of photons. Rev. Sci. Instrum. 86(7), 073113 (2015)","journal-title":"Rev. Sci. Instrum."},{"key":"2936_CR6","first-page":"595","volume":"47","author":"A Stefanov","year":"2000","unstructured":"Stefanov, A., Gisin, N., Guinnard, O., Guinnard, L., Zbinden, H.: Optical quantum random number generator. J. Mod. Opt. 47, 595\u2013598 (2000)","journal-title":"J. Mod. Opt."},{"issue":"25","key":"2936_CR7","doi-asserted-by":"publisher","first-page":"32788","DOI":"10.1364\/OE.26.032788","volume":"26","author":"MA Wayne","year":"2018","unstructured":"Wayne, M.A., Migdall, A.L., Levine, Z.H., Bienfang, J.C.: A post-processing-free single-photon random number generator with ultra-low latency. Opt. Express 26(25), 32788\u201332801 (2018)","journal-title":"Opt. Express"},{"key":"2936_CR8","doi-asserted-by":"publisher","first-page":"023820","DOI":"10.1103\/PhysRevA.83.023820","volume":"83","author":"M Ren","year":"2011","unstructured":"Ren, M., Wu, E., Liang, Y., Jian, Y., Guang, W., Zeng, H.: Quantum random-number generator based on a photon-number-resolving detector. Phys. Rev. A 83, 023820 (2011)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"2936_CR9","doi-asserted-by":"publisher","first-page":"043105","DOI":"10.1063\/1.5078547","volume":"90","author":"Z Zheng","year":"2019","unstructured":"Zheng, Z., Zhang, Y., Huang, W., Yu, S., Guo, H.: 6 Gbps real-time optical quantum random number generator based on vacuum fluctuation. Rev. Sci. Instrum. 90(4), 043105 (2019)","journal-title":"Rev. Sci. Instrum."},{"key":"2936_CR10","unstructured":"Gehring, T., Lupo, C., Kordts, A., Nikolic, D.S., Jain, N., Pedersen, T.B., Pirandola, S., Andersen, U.\u00a0L. 8 GBit\/s real-time quantum random number generator with non-iid samples. arXiv preprint arXiv:1812.05377 (2018)"},{"key":"2936_CR11","doi-asserted-by":"crossref","unstructured":"Shakhovoy, R., Sych, D., Sharoglazova, V., Udaltsov, A., Fedorov, A., Kurochkin, Y.: Quantum noise extraction from the interference of laser pulses in optical quantum random number generator. arXiv preprint arXiv:1910.00219 (2019)","DOI":"10.1364\/OE.380156"},{"key":"2936_CR12","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1364\/OL.34.001876","volume":"34","author":"W Wei","year":"2009","unstructured":"Wei, W., Guo, H.: Bias-free true random-number generator. Opt. Lett. 34, 1876 (2009)","journal-title":"Opt. Lett."},{"issue":"6","key":"2936_CR13","doi-asserted-by":"publisher","first-page":"618","DOI":"10.3390\/e22060618","volume":"22","author":"M Huang","year":"2020","unstructured":"Huang, M., Chen, Z., Zhang, Y., Guo, H.: A Gaussian-distributed quantum random number generator using vacuum shot noise. Entropy 22(6), 618 (2020)","journal-title":"Entropy"},{"issue":"7","key":"2936_CR14","doi-asserted-by":"publisher","first-page":"2431","DOI":"10.3390\/app10072431","volume":"10","author":"M Huang","year":"2020","unstructured":"Huang, M., Chen, Z., Zhang, Y., Guo, H.: A phase fluctuation based practical quantum random number generator scheme with delay-free structure. Appl. Sci. 10(7), 2431 (2020)","journal-title":"Appl. Sci."},{"issue":"1","key":"2936_CR15","doi-asserted-by":"publisher","first-page":"012422","DOI":"10.1103\/PhysRevA.102.012422","volume":"102","author":"W Huang","year":"2020","unstructured":"Huang, W., Zhang, Y., Zheng, Z., Li, Y., Xu, B., Yu, S.: Practical security analysis of a continuous-variable quantum random-number generator with a noisy local oscillator. Phys. Rev. A 102(1), 012422 (2020)","journal-title":"Phys. Rev. A"},{"issue":"7291","key":"2936_CR16","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1038\/nature09008","volume":"464","author":"S Pironio","year":"2010","unstructured":"Pironio, S., Ac\u00edn, A., Massar, S., de\u00a0La Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell\u2019s theorem. Nature 464(7291), 1021 (2010)","journal-title":"Nature"},{"issue":"1","key":"2936_CR17","doi-asserted-by":"publisher","first-page":"010503","DOI":"10.1103\/PhysRevLett.120.010503","volume":"120","author":"Y Liu","year":"2018","unstructured":"Liu, Y., Yuan, X., Li, M., Zhang, W., Zhao, Q., Zhong, J., Cao, Y., Li, Y., Chen, L., Li, H., Peng, T., Chen, Y., Peng, C., Shi, S., Wang, Z., You, L., Ma, X., Fan, J., Zhang, Q., Pan, J.: High-speed device-independent quantum random number generation without a detection loophole. Phys. Rev. Lett. 120(1), 010503 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"2936_CR18","doi-asserted-by":"publisher","first-page":"060301","DOI":"10.1103\/PhysRevA.94.060301","volume":"94","author":"Y Nie","year":"2016","unstructured":"Nie, Y., Guan, J., Zhou, H., Zhang, Q., Ma, X., Zhang, J., Pan, J.W.: Experimental measurement-device-independent quantum random number generation. Phys. Rev. A 94, 060301 (2016)","journal-title":"Phys. Rev. A"},{"key":"2936_CR19","doi-asserted-by":"publisher","first-page":"125011","DOI":"10.1088\/1367-2630\/17\/12\/125011","volume":"17","author":"Z Cao","year":"2015","unstructured":"Cao, Z., Zhou, H., Ma, X.: Loss-tolerant measurement-device-independent quantum random number generation. New J. Phys. 17, 125011 (2015)","journal-title":"New J. Phys."},{"issue":"1","key":"2936_CR20","first-page":"011020","volume":"6","author":"Z Cao","year":"2016","unstructured":"Cao, Z., Zhou, H., Yuan, X., Ma, X.: Source-independent quantum random number generation. Phys. Rev. X 6(1), 011020 (2016)","journal-title":"Phys. Rev. X"},{"issue":"6","key":"2936_CR21","doi-asserted-by":"publisher","first-page":"062326","DOI":"10.1103\/PhysRevA.99.062326","volume":"99","author":"PR Smith","year":"2019","unstructured":"Smith, P.R., Marangon, D.G., Lucamarini, M., Yuan, Z.L., Shields, A.J.: Simple source device-independent continuous-variable quantum random number generator. Phys. Rev. A 99(6), 062326 (2019)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"2936_CR22","doi-asserted-by":"publisher","first-page":"060503","DOI":"10.1103\/PhysRevLett.118.060503","volume":"118","author":"DG Marangon","year":"2017","unstructured":"Marangon, D.G., Vallone, G., Villoresi, P.: Source-device-independent ultrafast quantum random number generation. Phys. Rev. Lett. 118(6), 060503 (2017)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"2936_CR23","doi-asserted-by":"publisher","first-page":"025013","DOI":"10.1088\/2058-9565\/ab0fd9","volume":"4","author":"B Xu","year":"2019","unstructured":"Xu, B., Chen, Z., Li, Z., Yang, J., Qi, S., Huang, W., Zhang, Y., Guo, H.: High speed continuous variable source-independent quantum random number generation. Quantum Sci. Technol. 4(2), 025013 (2019)","journal-title":"Quantum Sci. Technol."},{"issue":"1","key":"2936_CR24","doi-asserted-by":"publisher","first-page":"5365","DOI":"10.1038\/s41467-018-07585-0","volume":"9","author":"M Avesani","year":"2018","unstructured":"Avesani, M., Marangon, D.G., Vallone, G., Villoresi, P.: Source-device-independent heterodyne-based quantum random number generator at 17 Gbps. Nat. Commun. 9(1), 5365 (2018)","journal-title":"Nat. Commun."},{"issue":"15","key":"2936_CR25","doi-asserted-by":"publisher","first-page":"22388","DOI":"10.1364\/OE.396461","volume":"28","author":"Z Zheng","year":"2020","unstructured":"Zheng, Z., Zhang, Y., Huang, M., Chen, Z., Yu, S., Guo, H.: Bias-free source-independent quantum random number generator. Opt. Express 28(15), 22388\u201322398 (2020)","journal-title":"Opt. Express"},{"issue":"5","key":"2936_CR26","doi-asserted-by":"publisher","first-page":"052327","DOI":"10.1103\/PhysRevA.90.052327","volume":"90","author":"G Vallone","year":"2014","unstructured":"Vallone, G., Marangon, D.G., Tomasin, M., Villoresi, P.: Quantum randomness certified by the uncertainty principle. Phys. Rev. A 90(5), 052327 (2014)","journal-title":"Phys. Rev. A"},{"key":"2936_CR27","doi-asserted-by":"crossref","unstructured":"Wang, X., Zhang, Y., Yu, S., Guo, H.: High-speed implementation of length-compatible privacy amplification in continuous-variable quantum key distribution. IEEE Photonics J. 10(3), 1\u20139 (2018)","DOI":"10.1109\/JPHOT.2018.2835767"},{"key":"2936_CR28","doi-asserted-by":"publisher","first-page":"21482","DOI":"10.1109\/ACCESS.2019.2896259","volume":"7","author":"Q Li","year":"2019","unstructured":"Li, Q., Yan, B.-Z., Mao, H.-K., Xue, X.-F., Han, Q., Guo, H.: High-speed and adaptive fpga-based privacy amplification in quantum key distribution. IEEE Access 7, 21482\u201321490 (2019)","journal-title":"IEEE Access"},{"issue":"6","key":"2936_CR29","doi-asserted-by":"publisher","first-page":"062343","DOI":"10.1103\/PhysRevA.81.062343","volume":"81","author":"A Leverrier","year":"2010","unstructured":"Leverrier, A., Grosshans, F., Grangier, P.: Finite-size analysis of a continuous-variable quantum key distribution. Phys. Rev. A 81(6), 062343 (2010)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"2936_CR30","doi-asserted-by":"publisher","first-page":"032309","DOI":"10.1103\/PhysRevA.86.032309","volume":"86","author":"P Jouguet","year":"2012","unstructured":"Jouguet, P., Kunz-Jacques, S., Diamanti, E., Leverrier, A.: Analysis of imperfections in practical continuous-variable quantum key distribution. Phys. Rev. A 86(3), 032309 (2012)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"2936_CR31","doi-asserted-by":"publisher","first-page":"042334","DOI":"10.1103\/PhysRevA.96.042334","volume":"96","author":"X Zhang","year":"2017","unstructured":"Zhang, X., Zhang, Y., Zhao, Y., Wang, X., Yu, S., Guo, H.: Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution. Phys. Rev. A 96(4), 042334 (2017)","journal-title":"Phys. Rev. A"},{"issue":"2053","key":"2936_CR32","first-page":"207","volume":"461","author":"I Devetak","year":"2005","unstructured":"Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. P. Roy. Soc. A-Math. Phy. 461(2053), 207\u2013235 (2005)","journal-title":"P. Roy. Soc. A-Math. Phy."},{"key":"2936_CR33","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Chen, Z., Pirandola, S., Wang, X., Zhou, C., Chu, B., Zhao, Y., Xu, B., Yu, S., Guo, H.: Long-distance continuous-variable quantum key distribution over 202.81 km of fiber. Phys. Rev. Lett. 125(1), 010502 (2020)","DOI":"10.1103\/PhysRevLett.125.010502"},{"issue":"3","key":"2936_CR34","doi-asserted-by":"publisher","first-page":"035006","DOI":"10.1088\/2058-9565\/ab19d1","volume":"4","author":"Y Zhang","year":"2019","unstructured":"Zhang, Y., Li, Z., Chen, Z., Weedbrook, C., Zhao, Y., Wang, X., Huang, Y., Xu, C., Zhang, X., Wang, Z., et al.: Continuous-variable QKD over 50 km commercial fiber. Quantum Sci. Technol. 4(3), 035006 (2019)","journal-title":"Quantum Sci. Technol."},{"key":"2936_CR35","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhang, Y., Li, Z., Yu, S., Guo, H.: 1.2-GHz balanced homodyne detector for continuous-variable quantum information technology. IEEE Photonics J. 10(5), 1\u201310 (2018)","DOI":"10.1109\/JPHOT.2018.2866514"},{"issue":"8","key":"2936_CR36","doi-asserted-by":"publisher","first-page":"080502","DOI":"10.1103\/PhysRevLett.96.080502","volume":"96","author":"MM Wolf","year":"2006","unstructured":"Wolf, M.M., Giedke, G., Cirac, J.I.: Extremality of Gaussian quantum states. Phys. Rev. Lett. 96(8), 080502 (2006)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"2936_CR37","doi-asserted-by":"publisher","first-page":"062327","DOI":"10.1103\/PhysRevA.87.062327","volume":"87","author":"X Ma","year":"2013","unstructured":"Ma, X., Xu, F., Xu, H., Tan, X., Qi, B., Lo, H.-K.: Postprocessing for quantum random-number generators: entropy evaluation and randomness extraction. Phys. Rev. A 87(6), 062327 (2013)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"2936_CR38","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1073\/pnas.42.1.43","volume":"42","author":"M Rosenblatt","year":"1956","unstructured":"Rosenblatt, M.: A central limit theorem and a strong mixing condition. P. Natl. Acad. Sci. USA 42(1), 43 (1956)","journal-title":"P. Natl. Acad. Sci. USA"},{"issue":"4","key":"2936_CR39","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1137\/0118065","volume":"18","author":"MD Springer","year":"1970","unstructured":"Springer, M.D., Thompson, W.E.: The distribution of products of beta, gamma and Gaussian random variables. SIAM J. Appl. Math. 18(4), 721\u2013737 (1970)","journal-title":"SIAM J. Appl. Math."},{"key":"2936_CR40","doi-asserted-by":"crossref","unstructured":"Drahi, D., Walk, N., Hoban, M.J., Kolthammer, W.S., Nunn, J., Barrett, J., Walmsley, I.A.: Certified quantum randomness from untrusted light. arXiv preprint arXiv:1905.09665 (2019)","DOI":"10.1103\/PhysRevX.10.041048"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02936-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-020-02936-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02936-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T08:39:42Z","timestamp":1612946382000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-020-02936-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["2936"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02936-7","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"19 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"15"}}