OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20665–20672

True random numbers from amplified quantum vacuum

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri  »View Author Affiliations

Optics Express, Vol. 19, Issue 21, pp. 20665-20672 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (872 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.

© 2011 OSA

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(230.0230) Optical devices : Optical devices
(270.0270) Quantum optics : Quantum optics

ToC Category:
Quantum Optics

Original Manuscript: July 8, 2011
Revised Manuscript: August 8, 2011
Manuscript Accepted: September 1, 2011
Published: October 3, 2011

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, "True random numbers from amplified quantum vacuum," Opt. Express 19, 20665-20672 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Galton, “Dice for statistical experiments,” Nature 42, 13–14 (1890). [CrossRef]
  2. R. Corporation, ed., A Million Random Digits with 100,000 Normal Deviates (The Free Press, 1955).
  3. T. Kanai, M. Tarui, and Y. Yamada, “Random number generator,” International patent WO2010090328 (2009).
  4. G. Ribordy and O. Guinnard, “Method and apparatus for generating true random numbers by way of a quantum optics process,” US patent 2007127718 (2007).
  5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]
  6. N. Cerf and L.-P. Lamooureux, “Network distributed quantum random number generation,” International patent GB2473078 (2009).
  7. N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, Inc., 2010).
  8. N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statist. Assoc. 44, 335–341 (1949). [CrossRef]
  9. S. Banks, P. Beadling, and A. Ferencz, “FPGA Implementation of Pseudo Random Number Generators for Monte Carlo Methods in Quantitative Finance,” in Proceedings of the 2008 International Conference on Reconfigurable, Computing and FPGAs, RECONFIG’08, (IEEE, 2008), pp. 271–276. [CrossRef]
  10. S. Pironio, A. Acin, S. Massar, A. B. de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010). [CrossRef] [PubMed]
  11. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675–1680 (2000). [CrossRef]
  12. O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” Appl. Opt. 48, 1774–1778 (2009). [CrossRef] [PubMed]
  13. M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007). [CrossRef] [PubMed]
  14. P. Bronner, A. Strunz, C. Silberhorn, and J. P. Meyn, “Demonstrating quantum random with single photons,” Eur. J. Phys. 30, 1189–1200 (2009). [CrossRef]
  15. M. Wayne and P. Kwiat, “Low-bias high-speed quantum number generator via shaped optical pulses,” Opt. Express 18, 9351–9357 (2010). [CrossRef] [PubMed]
  16. M. Fürst, H. Weier, S. Nauerth, D. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express 18, 13029–13037 (2010). [CrossRef] [PubMed]
  17. M. Wahl, M. Leifgen, M. Berlin, T. Rhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011). [CrossRef]
  18. C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4, 711–715 (2010). [CrossRef]
  19. T. Symul, S. M. Assad, and P. K. Lam, “Real time demonstration of high bitrate quantum random number generation with coherent laser light,” Appl. Phys. Lett. 98, 231103 (2011). [CrossRef]
  20. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008). [CrossRef]
  21. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010). [CrossRef] [PubMed]
  22. H. Guo, W. Tang, Y. Liu, and W. Wei, “Truly random number generation based on measurement of phase noise of a laser,” Phys. Rev. E 81, 051137 (2010). [CrossRef]
  23. P. R. Tapster and P. M. Gorman, “Apparatus and Method for Generating Random Numbers,” US patent 2009013019 (2009).
  24. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984). [CrossRef]
  25. M. D. Sturge, “Optical absorption of gallium arsenide between 0.6 and 2.75 ev,” Phys. Rev. 127, 768–773 (1962). [CrossRef]
  26. Y. Suematsu and S. Arai, “Single-mode semiconductor lasers for long-wavelength optical fiber communications and dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1436–1449 (2000). [CrossRef]
  27. P. Barreto and V. Rijmen, “The Whirlpool hashing fFunction,” pheattarchive.emporia.edu (2010).
  28. Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992). [CrossRef]
  29. N. Nisan and A. Ta-Shma, “Extracting randomness: a survey and new constructions,” J. Comput. Syst. Sci. 58, 148–173 (1999). [CrossRef]
  30. P. L’Ecuyer and R. Simard, “TestU01: AC library for empirical testing of random number generators,” ACM Trans. Math. Softw. 33, 1–40 (2007).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited