Abstract

Random number sequences are a critical resource in modern information processing systems, with applications in cryptography, numerical simulation, and data sampling. We introduce a quantum random number generator based on the measurement of pulse energy quantum fluctuations in Stokes light generated by spontaneously-initiated stimulated Raman scattering. Bright Stokes pulse energy fluctuations up to five times the mean energy are measured with fast photodiodes and converted to unbiased random binary strings. Since the pulse energy is a continuous variable, multiple bits can be extracted from a single measurement. Our approach can be generalized to a wide range of Raman active materials; here we demonstrate a prototype using the optical phonon line in bulk diamond.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Hayes, “Randomness as a resource,” Am. Sci. 89, 300–304 (2001).
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [Crossref]
  3. S. L. Lohr, Sampling: Design and Analysis (Cengage Learning, 2010).
  4. N. Metropolis and S. Ulam, “The Monte Carlo method,”J. Am. Stat. Assoc. 44, 335–341 (1949).
    [Crossref] [PubMed]
  5. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).
  6. 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]
  7. Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
    [Crossref]
  8. 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]
  9. 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]
  10. 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]
  11. 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).
    [Crossref] [PubMed]
  12. F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20, 12366–12377 (2012).
    [Crossref] [PubMed]
  13. A. Marandi, N. C. Leindecker, K. L. Vodopyanov, and R. L. Byer, “All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators,” Opt. Express 20, 19322–19330 (2012).
    [Crossref] [PubMed]
  14. S. Pironio, A. Acín, S. Massar, A. Boyer 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]
  15. M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
    [Crossref] [PubMed]
  16. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
    [Crossref]
  17. W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett. 34, 1876–1878 (2009).
    [Crossref] [PubMed]
  18. M. Fürst, H. Weier, S. Nauerth, D. G. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express 18, 13029–13037 (2010).
    [Crossref] [PubMed]
  19. M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
    [Crossref]
  20. M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]
  21. H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
    [Crossref]
  22. P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
    [Crossref]
  23. H. Krawczyk, “LFSR-based hashing and authentication,” in “Advances in Cryptology - CRYPTO’94,”, vol. 839 of Lecture Notes in Computer Science, Y. Desmedt, ed. (Springer, 1994), pp. 129–139.
  24. X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
    [Crossref]
  25. A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
    [Crossref]
  26. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
    [Crossref]
  27. S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
    [Crossref] [PubMed]
  28. D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
    [Crossref] [PubMed]
  29. M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
    [Crossref] [PubMed]
  30. M. G. Raymer, K. Rza̧żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
    [Crossref] [PubMed]
  31. I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
    [Crossref]
  32. I. A. Walmsley and M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
    [Crossref] [PubMed]
  33. J. Mostowski and B. d. z. Sobolewska, “Transverse effects in stimulated Raman scattering,” Phys. Rev. A 30, 610–612 (1984).
    [Crossref]
  34. M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
    [Crossref] [PubMed]
  35. F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
    [Crossref]
  36. K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
    [Crossref]
  37. K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
    [Crossref]
  38. K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
    [Crossref]
  39. G. Marsaglia, “Diehard battery of tests of randomness,” www.stat.fsu.edu/pub/diehard/ (1995).
  40. J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), Chap. 15, p. 15.1.
  41. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [Crossref] [PubMed]

2013 (2)

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

2012 (2)

2011 (6)

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).
[Crossref] [PubMed]

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

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]

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

2010 (7)

M. Fürst, H. Weier, S. Nauerth, D. G. Marangon, C. Kurtsiefer, and H. Weinfurter, “High speed optical quantum random number generation,” Opt. Express 18, 13029–13037 (2010).
[Crossref] [PubMed]

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]

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]

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]

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[Crossref]

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

2009 (1)

2008 (2)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

2002 (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

2001 (1)

B. Hayes, “Randomness as a resource,” Am. Sci. 89, 300–304 (2001).

2000 (1)

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

1993 (1)

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

1991 (2)

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[Crossref] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

1986 (1)

I. A. Walmsley and M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[Crossref] [PubMed]

1985 (1)

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

1984 (1)

J. Mostowski and B. d. z. Sobolewska, “Transverse effects in stimulated Raman scattering,” Phys. Rev. A 30, 610–612 (1984).
[Crossref]

1983 (1)

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[Crossref]

1982 (2)

K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
[Crossref]

M. G. Raymer, K. Rza̧żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[Crossref] [PubMed]

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

1979 (1)

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[Crossref]

1970 (1)

H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[Crossref]

1949 (1)

N. Metropolis and S. Ulam, “The Monte Carlo method,”J. Am. Stat. Assoc. 44, 335–341 (1949).
[Crossref] [PubMed]

Acín, A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Andersen, U. L.

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]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Anzolin, G.

Assad, S. M.

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]

Bashkansky, M.

J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), Chap. 15, p. 15.1.

Belsley, M.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Berlin, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Boyer de la Giroday, A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Bustard, P. J.

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Byer, R. L.

Chi, Y.-M.

Curty, M.

Deng, D.-L.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Dong, R.

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]

Duan, L.-M.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

Fürst, M.

Gabriel, C.

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]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guinnard, L.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guinnard, O.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Guo, H.

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]

W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett. 34, 1876–1878 (2009).
[Crossref] [PubMed]

Hayes, B.

B. Hayes, “Randomness as a resource,” Am. Sci. 89, 300–304 (2001).

Hayes, D.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Jaksch, D.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Jian, Y.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

Jofre, M.

Kaiser, W.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[Crossref]

Kim, K.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Knight, J. C.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Krawczyk, H.

H. Krawczyk, “LFSR-based hashing and authentication,” in “Advances in Cryptology - CRYPTO’94,”, vol. 839 of Lecture Notes in Computer Science, Y. Desmedt, ed. (Springer, 1994), pp. 129–139.

Kuo, S. J.

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[Crossref] [PubMed]

Kurtsiefer, C.

Lam, P. K.

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]

Langford, N. K.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Laubereau, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[Crossref]

Lausten, R.

Lee, K. C.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Lee, K. H.

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Leindecker, N. C.

Leuchs, G.

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]

Lewenstein, M.

K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
[Crossref]

Liang, Y.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

Liu, Y.

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]

Lo, H.-K.

Lohr, S. L.

S. L. Lohr, Sampling: Design and Analysis (Cengage Learning, 2010).

Lorenz, V. O.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Luo, L.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Ma, X.

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20, 12366–12377 (2012).
[Crossref] [PubMed]

Manning, T. A.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Marandi, A.

Marangon, D. G.

Marquardt, C.

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]

Massar, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Matsukevich, D. N.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Mauerer, W.

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]

Maunz, P.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo method,”J. Am. Stat. Assoc. 44, 335–341 (1949).
[Crossref] [PubMed]

Michelberger, P.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Mitchell, M. W.

Moffatt, D.

Monroe, C.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Mostowski, J.

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

J. Mostowski and B. d. z. Sobolewska, “Transverse effects in stimulated Raman scattering,” Phys. Rev. A 30, 610–612 (1984).
[Crossref]

M. G. Raymer, K. Rza̧żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[Crossref] [PubMed]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

Nauerth, S.

Nunn, J.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Olivero, P.

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Olmschenk, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Penzkofer, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[Crossref]

Pironio, S.

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Prawer, S.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Pruneri, V.

Qi, B.

Qian, L.

Rahn, H.-J.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Raymer, M. G.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[Crossref] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[Crossref]

M. G. Raymer, K. Rza̧żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[Crossref] [PubMed]

K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
[Crossref]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

Reim, K.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

Reim, K. F.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Reintjes, J.

J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), Chap. 15, p. 15.1.

Ren, M.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Röhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Russell, P. S. J.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Rza¸zewski, K.

K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
[Crossref]

M. G. Raymer, K. Rza̧żewski, and J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71–73 (1982).
[Crossref] [PubMed]

Schmidt, H.

H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[Crossref]

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

Shen, Y.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[Crossref]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

Smithey, D. T.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[Crossref] [PubMed]

Sobolewska, B.

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

Sobolewska, B. d. z.

J. Mostowski and B. d. z. Sobolewska, “Transverse effects in stimulated Raman scattering,” Phys. Rev. A 30, 610–612 (1984).
[Crossref]

Spizziri, P.

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Spizzirri, P.

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

Sprague, M. R.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Stefanov, A.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Steinlechner, F.

Surmacz, K.

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Sussman, B. J.

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Sych, D.

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]

Symul, T.

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]

Tan, X.

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

Tang, W.

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]

Tian, L.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Torres, J. P.

Ulam, S.

N. Metropolis and S. Ulam, “The Monte Carlo method,”J. Am. Stat. Assoc. 44, 335–341 (1949).
[Crossref] [PubMed]

Um, M.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Vodopyanov, K. L.

Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Waldermann, F. C.

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Walmsley, I. A.

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

I. A. Walmsley and M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[Crossref] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[Crossref]

Wang, Y.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Wedding, K.

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

Wei, W.

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]

W. Wei and H. Guo, “Bias-free true random-number generator,” Opt. Lett. 34, 1876–1878 (2009).
[Crossref] [PubMed]

Weier, H.

Weinfurter, H.

Wittmann, C.

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]

Wu, E.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

Wu, G.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

P. J. Bustard, D. Moffatt, R. Lausten, G. Wu, I. A. Walmsley, and B. J. Sussman, “Quantum random bit generation using stimulated Raman scattering,” Opt. Express 19, 25173–25180 (2011).
[Crossref]

Xu, F.

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20, 12366–12377 (2012).
[Crossref] [PubMed]

Xu, H.

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20, 12366–12377 (2012).
[Crossref] [PubMed]

Yangchao, S.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Zeng, H.

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

Zhang, J.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Zhang, X.

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Zheng, H.

Zou, H.

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[Crossref]

Am. Sci. (1)

B. Hayes, “Randomness as a resource,” Am. Sci. 89, 300–304 (2001).

Appl. Phys. Lett. (3)

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]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93, 031109 (2008).
[Crossref]

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, 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]

Diamond Relat. Mater. (1)

K. C. Lee, B. J. Sussman, J. Nunn, V. O. Lorenz, K. Reim, D. Jaksch, I. A. Walmsley, P. Spizzirri, and S. Prawer, “Comparing phonon dephasing lifetimes in diamond using transient coherent ultrafast phonon spectroscopy,” Diamond Relat. Mater. 19, 1289–1295 (2010).
[Crossref]

J. Am. Stat. Assoc. (1)

N. Metropolis and S. Ulam, “The Monte Carlo method,”J. Am. Stat. Assoc. 44, 335–341 (1949).
[Crossref] [PubMed]

J. Appl. Phys. (1)

H. Schmidt, “Quantum mechanical random number generator,” J. Appl. Phys. 41, 462–468 (1970).
[Crossref]

J. Mod. Opt. (1)

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595–598 (2000).

Nat. Photonics (2)

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]

K. C. Lee, B. J. Sussman, M. R. Sprague, P. Michelberger, K. F. Reim, J. Nunn, N. K. Langford, P. J. Bustard, D. Jaksch, and I. A. Walmsley, “Macroscopic non-classical states and terahertz quantum processing in room-temperature diamond,” Nat. Photonics 6, 41–44 (2011).
[Crossref]

Nature (1)

S. Pironio, A. Acín, S. Massar, A. Boyer 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]

Opt. Commun. (1)

K. Rza̧żewski, M. Lewenstein, and M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady-state regime,” Opt. Commun. 43, 451–454 (1982).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. A (9)

M. Belsley, D. T. Smithey, K. Wedding, and M. G. Raymer, “Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering,” Phys. Rev. A 48, 1514–1525 (1993).
[Crossref] [PubMed]

Y. Shen, L. Tian, and H. Zou, “Practical quantum random number generator based on measuring the shot noise of vacuum states,” Phys. Rev. A 81, 063814 (2010).
[Crossref]

M. Ren, E. Wu, Y. Liang, Y. Jian, G. Wu, and H. Zeng, “Quantum random-number generator based on a photon-number-resolving detector,” Phys. Rev. A 83, 023820 (2011).
[Crossref]

X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, “Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction,” Phys. Rev. A 87, 062327 (2013).
[Crossref]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980–1993 (1981).
[Crossref]

S. J. Kuo, D. T. Smithey, and M. G. Raymer, “Spatial interference of macroscopic light fields from independent Raman sources,” Phys. Rev. A 43, 4083–4086 (1991).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382–390 (1986).
[Crossref] [PubMed]

J. Mostowski and B. d. z. Sobolewska, “Transverse effects in stimulated Raman scattering,” Phys. Rev. A 30, 610–612 (1984).
[Crossref]

M. G. Raymer, I. A. Walmsley, J. Mostowski, and B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332–344 (1985).
[Crossref] [PubMed]

Phys. Rev. B (1)

F. C. Waldermann, B. J. Sussman, J. Nunn, V. O. Lorenz, K. C. Lee, K. Surmacz, K. H. Lee, D. Jaksch, I. A. Walmsley, P. Spizziri, P. Olivero, and S. Prawer, “Measuring phonon dephasing with ultrafast pulses using Raman spectral interference,” Phys. Rev. B 78, 155201 (2008).
[Crossref]

Phys. Rev. E (1)

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]

Phys. Rev. Lett. (2)

D. T. Smithey, M. Belsley, K. Wedding, and M. G. Raymer, “Near quantum-limited phase memory in a Raman amplifier,” Phys. Rev. Lett. 67, 2446–2449 (1991).
[Crossref] [PubMed]

I. A. Walmsley and M. G. Raymer, “Observation of macroscopic quantum fluctuations in stimulated Raman scattering,” Phys. Rev. Lett. 50, 962–965 (1983).
[Crossref]

Prog. Quantum Electron. (1)

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron. 6, 55–140 (1979).
[Crossref]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Sci. Rep. (1)

M. Um, X. Zhang, J. Zhang, Y. Wang, S. Yangchao, D.-L. Deng, L.-M. Duan, and K. Kim, “Experimental certification of random numbers via quantum contextuality,” Sci. Rep. 3, 1627 (2013).
[Crossref] [PubMed]

Science (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[Crossref] [PubMed]

Other (4)

S. L. Lohr, Sampling: Design and Analysis (Cengage Learning, 2010).

H. Krawczyk, “LFSR-based hashing and authentication,” in “Advances in Cryptology - CRYPTO’94,”, vol. 839 of Lecture Notes in Computer Science, Y. Desmedt, ed. (Springer, 1994), pp. 129–139.

G. Marsaglia, “Diehard battery of tests of randomness,” www.stat.fsu.edu/pub/diehard/ (1995).

J. Reintjes and M. Bashkansky, Handbook of Optics, Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw-Hill Professional, 2010), Chap. 15, p. 15.1.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Λ-level diagram for Stokes Raman scattering in diamond. Inelastic scattering annihilates the pump photon at 532 nm, creating an optical phonon in the diamond and a red-shifted Stokes photon at 573 nm.

Fig. 2
Fig. 2

Experimental setup: the pump pulse is focussed into a diamond plate, generating a Stokes sideband by SISRS. The Stokes pulse is spectrally-filtered from the pump, and its energy is measured by photodiode PD2. Part of the pump pulse energy is separated using a beamsplitter in front of the diamond, and is measured by photodiode PD1.

Fig. 3
Fig. 3

Plot of the measured Stokes pulse energy distribution P(WS|Wp) as a function of the normalized Stokes pulse energy WS/〈WS〉 for a single pump pulse energy value Wp = 〈Wp〉.

Tables (1)

Tables Icon

Table 1 Results of the Diehard statistical tests applied to the Raman random number bit strings. The p-values are within the significance interval 0.01 < α < 0.99, indicating that the bit strings pass all the tests.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

H ( W S ) = log 2 [ max w S P ( W S = w S ) ] ,
H ˜ ( W S | W p = w p ) = log 2 [ max w S P ˜ ( W S = w S | W p = w p ) ] ,

Metrics