{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T03:44:58Z","timestamp":1773200698295,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T00:00:00Z","timestamp":1682640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"United States Defense Advanced Research Projects Agency (DARPA)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present the theory, architecture, and performance characteristics of a quantum random number generator (QRNG) which operates in a PCI express form factor-compatible plug-and-play design. The QRNG relies on a thermal light source (in this case, amplified spontaneous emission), which exhibits photon bunching according to the Bose\u2013Einstein (BE) statistics. We demonstrate that 98.7% of the unprocessed random bit stream min-entropy is traceable to the BE (quantum) signal. The classical component is then removed using a non-reuse shift-XOR protocol, and the final random numbers are generated at a 200 Mbps rate and shown to pass the statistical randomness test suites FIPS 140-2, Alphabit, SmallCrush, DIEHARD, and Rabbit of the TestU01 library.<\/jats:p>","DOI":"10.3390\/e25050731","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T04:36:15Z","timestamp":1682656575000},"page":"731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Development of a High Min-Entropy Quantum Random Number Generator Based on Amplified Spontaneous Emission"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2464-8042","authenticated-orcid":false,"given":"Charlotte K.","family":"Duda","sequence":"first","affiliation":[{"name":"Material Physics & Applications, Los Alamos National Lab, P.O. Box 1663, Los Alamos, NM 87545, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4676-1836","authenticated-orcid":false,"given":"Kristina A.","family":"Meier","sequence":"additional","affiliation":[{"name":"Intelligence & Space Research, Los Alamos National Lab, P.O. Box 1663, Los Alamos, NM 87545, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5989-5951","authenticated-orcid":false,"given":"Raymond T.","family":"Newell","sequence":"additional","affiliation":[{"name":"Material Physics & Applications, Los Alamos National Lab, P.O. Box 1663, Los Alamos, NM 87545, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124001","DOI":"10.1088\/1361-6633\/aa8731","article-title":"Randomness in Quantum Mechanics: Philosophy, Physics and Technology","volume":"80","author":"Bera","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_2","unstructured":"Ananthaswamy, A. (2023, March 11). How to Turn a Quantum Computer Into the Ultimate Randomness Generator; 2019, Quanta Magazine, New York, NY, USA. Available online: https:\/\/www.quantamagazine.org\/how-to-turn-a-quantum-computer-into-the-ultimate-randomness-generator-20190619\/."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1007\/11424826_67","article-title":"Obtaining True-Random Binary Numbers from a Weak Radioactive Source","volume":"Volume 3481","author":"Alkassar","year":"2005","journal-title":"Proceedings of the Computational Science and Its Applications\u2013ICCSA 2005"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1063\/1.1658698","article-title":"Quantum-Mechanical Random-Number Generator","volume":"41","author":"Schmidt","year":"1970","journal-title":"J. Appl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1515\/FREQ.1985.39.7-8.187","article-title":"Concept for a High Performance Random Number Generator Based on Physical Random Phenomena","volume":"39","author":"Gude","year":"1985","journal-title":"Frequenz"},{"key":"ref_6","unstructured":"Petrie, C., and Connelly, J. (June, January 31). A noise-based random bit generator IC for applications in cryptography. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (ISCAS), Monterey, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1364\/OL.35.000312","article-title":"High-speed quantum random number generation by measuring phase noise of a single-mode laser","volume":"35","author":"Qi","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_8","first-page":"031056","article-title":"Quantum Random Number Generation on a Mobile Phone","volume":"4","author":"Sanguinetti","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1038\/nphoton.2010.197","article-title":"A generator for unique quantum random numbers based on vacuum states","volume":"4","author":"Gabriel","year":"2010","journal-title":"Nat. Photon"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1063\/1.1150518","article-title":"A fast and compact quantum random number generator","volume":"71","author":"Jennewein","year":"2000","journal-title":"Rev. Sci. Instruments"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9351","DOI":"10.1364\/OE.18.009351","article-title":"Low-bias high-speed quantum random number generator via shaped optical pulses","volume":"18","author":"Wayne","year":"2010","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"171105","DOI":"10.1063\/1.3578456","article-title":"An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements","volume":"98","author":"Wahl","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"051110","DOI":"10.1063\/1.4863224","article-title":"Practical and fast quantum random number generation based on photon arrival time relative to external reference","volume":"104","author":"Nie","year":"2014","journal-title":"Appl. Phys. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"063105","DOI":"10.1063\/1.4922417","article-title":"The generation of 68 Gbps quantum random number by measuring laser phase fluctuations","volume":"86","author":"Nie","year":"2015","journal-title":"Rev. Sci. Instruments"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1109\/LPT.2021.3088156","article-title":"16.8 Tb\/s True Random Number Generator Based on Amplified Spontaneous Emission","volume":"33","author":"Cao","year":"2021","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1006\/jcss.1997.1546","article-title":"Extracting Randomness: A Survey and New Constructions","volume":"58","author":"Nisan","year":"1999","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_17","unstructured":"Nordholt, J.E., Hughes, R.J., Newell, R.T., and Peterson, C.G. (2022). Quantum Random Number Generators. (US11442698B2)."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1038\/177027a0","article-title":"Correlation between Photons in two Coherent Beams of Light","volume":"177","author":"Brown","year":"1956","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1268776.1268777","article-title":"TestU01: A C library for empirical testing of random number generators","volume":"33","author":"Simard","year":"2007","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_20","unstructured":"Killmann, W., and Schindler, W. (2023, January 24). A Proposal for Functionality Classes for Random Number Generators. Available online: https:\/\/cosec.bit.uni-bonn.de\/fileadmin\/user_upload\/teaching\/15ss\/15ss-taoc\/01_AIS31_Functionality_classes_for_random_number_generators.pdf."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Barker, E.B., and Kelsey, J.M. (2015). Recommendation for Random Number Generation Using Deterministic Random Bit Generators.","DOI":"10.6028\/NIST.SP.800-90Ar1"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1364\/OL.23.001832","article-title":"Photon statistics of amplified spontaneous emission noise in a 10-Gbit\/s optically preamplified direct-detection receiver","volume":"23","author":"Wong","year":"1998","journal-title":"Opt. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1364\/OL.28.000152","article-title":"Photon statistics of amplified spontaneous emission in a dense wavelength-division multiplexing regime","volume":"28","author":"Pietralunga","year":"2003","journal-title":"Opt. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/731\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:25:26Z","timestamp":1760124326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/731"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,28]]},"references-count":23,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050731"],"URL":"https:\/\/doi.org\/10.3390\/e25050731","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,28]]}}}