Abstract

We present a high-speed random number generation scheme based on measuring the quantum phase noise of a single-mode laser operating at a low intensity level near the lasing threshold. A delayed self-heterodyning system has been developed to measure the random phase fluctuation. By actively stabilizing the phase of the interferometer, a random number generation rate of 500 Mbit/s has been demonstrated and the generated random numbers have passed all the DIEHARD tests.

© 2010 Optical Society of America

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  1. N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
    [CrossRef] [PubMed]
  2. B. Schneier, Applied Cryptography (Wiley, 1996).
  3. C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.
  4. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
    [CrossRef]
  5. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
    [CrossRef]
  6. http://www.idquantique.com.
  7. 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, Nat. Photonics 2, 728 (2008).
    [CrossRef]
  8. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
    [CrossRef] [PubMed]
  9. A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.
  10. C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
    [CrossRef]
  11. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford U. Press, 2007).
  12. M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
    [CrossRef]
  13. B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
    [CrossRef]
  14. http://www.stat.fsu.edu/pub/diehard/.

2009

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

2008

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

2003

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
[CrossRef]

2000

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

1982

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

1949

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Achleitner, U.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Amano, K.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Aviad, Y.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Barak, B.

B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
[CrossRef]

Bennett, C. H.

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

Brassard, G.

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

Chi, Y. -M.

A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.

Davis, P.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Epstein, M.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

Hars, L.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

Hirano, K.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Inoue, M.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Jennewein, T.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Kanter, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Krasinski, R.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

Kurashige, T.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Lo, H. -K.

A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.

Metropolis, N.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Naito, S.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Oowada, I.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Qi, B.

A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.

Qian, L.

A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.

Reidler, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Rosenbluh, M.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Rosner, M.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

Schneier, B.

B. Schneier, Applied Cryptography (Wiley, 1996).

Shaltiel, R.

B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
[CrossRef]

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Shiki, M.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Someya, H.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Tromer, E.

B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
[CrossRef]

Uchida, A.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Ulam, S.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Weihs, G.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Weinfurter, H.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford U. Press, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford U. Press, 2007).

Yoshimori, S.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Yoshimura, K.

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

Zeilinger, A.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Zheng, H.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

Appl. Phys. Lett.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. 93, 031109 (2008).
[CrossRef]

IEEE J. Quantum Electron.

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

J. Am. Stat. Assoc.

N. Metropolis and S. Ulam, J. Am. Stat. Assoc. 44, 335 (1949).
[CrossRef] [PubMed]

Lect. Notes Comput. Sci.

M. Epstein, L. Hars, R. Krasinski, M. Rosner and H. Zheng, Lect. Notes Comput. Sci. 2779, 152 (2003).
[CrossRef]

B. Barak, R. Shaltiel, and E. Tromer, Lect. Notes Comput. Sci. 2779, 166 (2003).
[CrossRef]

Nat. Photonics

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, Nat. Photonics 2, 728 (2008).
[CrossRef]

Phys. Rev. Lett.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. 71, 1675 (2000).
[CrossRef]

Other

http://www.stat.fsu.edu/pub/diehard/.

A preliminary version of our results has appeared in B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, in Proceedings of The 9th Asian Conference on Quantum Information Science (AQIS, 2009), pp. 64-65.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford U. Press, 2007).

B. Schneier, Applied Cryptography (Wiley, 1996).

C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175-179.

http://www.idquantique.com.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. L , 1550   nm DFB diode laser; P C 1 ,   P C 2 , polarization controllers; PM , phase modulator; C 1 , C 2 , fiber couplers; P D 1 , 5   GHz photodetector for random number generation; P D 2 , 1   MHz photo receiver for phase monitoring; D A Q 1 , 1   GS / s data acquisition card; D A Q 2 , 1   MS / s data acquisition card; Comp, desktop computer. The time delay difference resulting from the length imbalance Δ L is 650 ± 100   ps .

Fig. 2
Fig. 2

Spectral power density of electrical and phase noise. The solid-line, dot-line, and circle-line represent the spectral power densities of the detection system, the phase noise with a long delay ( T d = 650 ± 100   ps ) , and the phase noise with a short delay ( T d = 250 ± 100   ps ) , correspondingly.

Fig. 3
Fig. 3

Autocorrelations of the random number trains acquired at 1 Gbit/s. Note for Bin3, the equivalent random number generation rate is 500 Mbit/s.

Tables (1)

Tables Icon

Table 1 DIEHARD Test Results (500 Mbits/s)

Equations (3)

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

E ( t ) = E 0   exp { i [ ω 0 t + θ ( t ) ] } ,
S ( t ) cos [ ω 0 T d + Δ θ ( t , T d ) ] ,
[ Δ θ ( t , T d ) ] 2 = 2 T d τ c .

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