Abstract

We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators.

© 2010 OSA

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  1. “Ais 20: Functionality classes and evaluation methodology for deterministic random number generators, v2.0, bsi,” https://www.bsi.bund.de/cae/servlet/contentblob/478150/publicationFile/30276/ais20_pdf.pdf (1999).
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  4. W. Killmann and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect Notes Comput Sc 5154, 146–163 (2008).
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  5. B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).
  6. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
    [CrossRef] [PubMed]
  7. A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).
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    [CrossRef]
  9. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
    [CrossRef]
  10. 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]
  11. M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
    [CrossRef] [PubMed]
  12. S. Tisa and F. Zappa, “One-chip quantum random number generator” Proceedings SPIE 7236, 72360J (2009)
    [CrossRef]
  13. 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]
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    [CrossRef]
  15. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Optic. 47, 595–598 (2000).
  16. “Ais 31: Functionality classes and evaluation methodology for physical random number generators. v1.0,” (2001).
  17. W. Killmann and W. Schindler, “A proposal for: Functionality classes and evaluation methodology for true (physical) random number generators (v3.1).” https://www.bsi.bund.de/cae/servlet/contentblob/ 478134/publication-File/30230/trngk31e_pdf.pdf (2001).
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  19. R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
    [CrossRef]
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  21. R. G. Brown, “Dieharder test suite,” http://www.phy.duke.edu/ rgb/General/dieharder.php (2009).
  22. J. Kim and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
    [CrossRef]
  23. P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
    [CrossRef]
  24. R. Loudon, The quantum theory of light (Oxford University Press, 2000), third edition ed.
  25. R. Short and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett 51, 384 (1983).
    [CrossRef]
  26. A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
    [CrossRef]
  27. K. Omote, “Dead time effects in photon-counting distributions,” Nucl Instrum Methods 293, 582–588 (1990).
    [CrossRef]
  28. J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl Instrum Methods 117, 401–404 (1974).
    [CrossRef]
  29. D. E. Knuth, The Art of Computer Programming II (Addison-Wesley, 1998).
  30. N. H. Kuiper, “Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet. A 63, 38–47 (1962).

2010 (1)

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

2009 (4)

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

S. Tisa and F. Zappa, “One-chip quantum random number generator” Proceedings SPIE 7236, 72360J (2009)
[CrossRef]

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]

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]

W. Killmann and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect Notes Comput Sc 5154, 146–163 (2008).
[CrossRef]

2007 (1)

M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

2006 (1)

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

2000 (3)

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

C. Petrie and J. Connelly, “A noise-based ic random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications 47, 615–621 (2000).
[CrossRef]

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

1997 (1)

J. Kim and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

1994 (1)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

1990 (1)

K. Omote, “Dead time effects in photon-counting distributions,” Nucl Instrum Methods 293, 582–588 (1990).
[CrossRef]

1987 (1)

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
[CrossRef]

1983 (1)

R. Short and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett 51, 384 (1983).
[CrossRef]

1974 (1)

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl Instrum Methods 117, 401–404 (1974).
[CrossRef]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

1962 (1)

N. H. Kuiper, “Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet. A 63, 38–47 (1962).

Achleitner, U.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Alkassar, A.

A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).

Aviad, Y.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Bennet, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

Brown, R. G.

R. G. Brown, “Dieharder test suite,” http://www.phy.duke.edu/ rgb/General/dieharder.php (2009).

Che, Y.

B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).

Cho, Y.-W.

Connelly, J.

C. Petrie and J. Connelly, “A noise-based ic random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications 47, 615–621 (2000).
[CrossRef]

Dixon, A. R.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

Dynes, J. F.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[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]

Gisin, N.

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

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Guinnard, L.

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

Guinnard, O.

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

Jennewein, T.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Kanter, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Killmann, W.

W. Killmann and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect Notes Comput Sc 5154, 146–163 (2008).
[CrossRef]

W. Killmann and W. Schindler, “A proposal for: Functionality classes and evaluation methodology for true (physical) random number generators (v3.1).” https://www.bsi.bund.de/cae/servlet/contentblob/ 478134/publication-File/30230/trngk31e_pdf.pdf (2001).

Kim, J.

J. Kim and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Kim, Y.-H.

Knuth, D. E.

D. E. Knuth, The Art of Computer Programming II (Addison-Wesley, 1998).

Kuiper, N. H.

N. H. Kuiper, “Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet. A 63, 38–47 (1962).

Kwon, O.

Li, Y.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

Lo, H.-K.

B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).

Long, G.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

Loudon, R.

R. Loudon, The quantum theory of light (Oxford University Press, 2000), third edition ed.

Mandel, L.

R. Short and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett 51, 384 (1983).
[CrossRef]

Mueller, J. W.

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl Instrum Methods 117, 401–404 (1974).
[CrossRef]

Nicolay, T.

A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).

Omote, K.

K. Omote, “Dead time effects in photon-counting distributions,” Nucl Instrum Methods 293, 582–588 (1990).
[CrossRef]

Owens, P. C. M.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

Petrie, C.

C. Petrie and J. Connelly, “A noise-based ic random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications 47, 615–621 (2000).
[CrossRef]

Prionio, S.

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

Qi, B.

B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).

Qian, L.

B. Qi, Y. Che, H.-K. Lo, and L. Qian, “Experimental demonstration of a high speed quantum random number generation scheme based on measuring phase noise of a single mode laser,” arXiv.org 0908.3351 (2009).

Rarity, J. G.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
[CrossRef]

Reidler, I.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Rogina, B. M.

M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Rohe, M.

A. Alkassar, T. Nicolay, and M. Rohe, Obtaining true random binary numbers from a weak radioactive source (Springer-Verlag: Computational Science and its applitcations, 2005).

Rosenbluh, M.

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Satchell, J. S.

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
[CrossRef]

Schindler, W.

W. Killmann and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect Notes Comput Sc 5154, 146–163 (2008).
[CrossRef]

W. Killmann and W. Schindler, “A proposal for: Functionality classes and evaluation methodology for true (physical) random number generators (v3.1).” https://www.bsi.bund.de/cae/servlet/contentblob/ 478134/publication-File/30230/trngk31e_pdf.pdf (2001).

Sharpe, A. W.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[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]

Shields, A. J.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[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]

Short, R.

R. Short and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett 51, 384 (1983).
[CrossRef]

Soto, J.

J. Soto, “Statistical testing of random number generators,” Proc. 22nd National Information Systems Security Conference (1999).

Stefanov, A.

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

Stipcevic, M.

M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Tapster, P. R.

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
[CrossRef]

Tisa, S.

S. Tisa and F. Zappa, “One-chip quantum random number generator” Proceedings SPIE 7236, 72360J (2009)
[CrossRef]

Wang, P.

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

Weihs, G.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Weinfurter, H.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Yamamoto, Y.

J. Kim and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Yuan, Z. L.

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[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]

Zappa, F.

S. Tisa and F. Zappa, “One-chip quantum random number generator” Proceedings SPIE 7236, 72360J (2009)
[CrossRef]

Zbinden, H.

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

Zeilinger, A.

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (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]

A. R. Dixon, J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Bennet, and A. J. Shields, “Ultrashort dead time of photon-counting InGaAs avalanche photodiodes,” Appl. Phys. Lett. 94, 231113 (2009).
[CrossRef]

EPL (Europhysics Letters) (1)

P. R. Tapster, J. G. Rarity, and J. S. Satchell, “Generation of sub-poissonian light by high-efficiency light-emitting diodes,” EPL (Europhysics Letters) 4, 293–299 (1987).
[CrossRef]

IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications (1)

C. Petrie and J. Connelly, “A noise-based ic random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications 47, 615–621 (2000).
[CrossRef]

J. Appl. Phys. (1)

P. Wang, G. Long, and Y. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
[CrossRef]

J. Mod. Opt. (1)

J. G. Rarity, P. C. M. Owens, and P. R. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435 (1994).
[CrossRef]

J. Mod. Optic. (1)

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

Lect Notes Comput Sc (1)

W. Killmann and W. Schindler, “A design for a physical rng with robust entropy estimators,” Lect Notes Comput Sc 5154, 146–163 (2008).
[CrossRef]

Nature (1)

S. Prionio, “Random numbers certified by Bell’s theorem,” Nature 464, 1021–1024 (2010).
[CrossRef]

Nucl Instrum Methods (2)

K. Omote, “Dead time effects in photon-counting distributions,” Nucl Instrum Methods 293, 582–588 (1990).
[CrossRef]

J. W. Mueller, “Some formulae for a dead-time-distorted poisson process,” Nucl Instrum Methods 117, 401–404 (1974).
[CrossRef]

Phys. Rev. (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Phys. Rev. B (1)

J. Kim and Y. Yamamoto, “Theory of noise in p-n junction light emitters,” Phys. Rev. B 55, 9949 (1997).
[CrossRef]

Phys. Rev. Lett (1)

R. Short and L. Mandel, “Observation of sub-poissonian photon statistics,” Phys. Rev. Lett 51, 384 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Proc. Kon. Ned. Aka Wet. (1)

N. H. Kuiper, “Tests concerning random points on a circle,” Proc. Kon. Ned. Aka Wet. A 63, 38–47 (1962).

Proceedings SPIE (1)

S. Tisa and F. Zappa, “One-chip quantum random number generator” Proceedings SPIE 7236, 72360J (2009)
[CrossRef]

Rev. Sci. Instr. (1)

T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instr. 71, 1675–1680 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
[CrossRef] [PubMed]

Other (10)

D. E. Knuth, The Art of Computer Programming II (Addison-Wesley, 1998).

R. Loudon, The quantum theory of light (Oxford University Press, 2000), third edition ed.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the setup (left) and picture of the fully integrated quantum random number generator (right). The main components are a light emitting diode (LED) mounted on the entrance window of a photomultiplier tube (PMT). The electrical pulses from the PMT are amplified (AMP) and fed into a threshold discriminator (ST). The signals are counted and processed by the FPGA, the resulting random bits are transferred to a PC via a USB connection. The total dimension of the housing is 22x16x8 cm3.

Fig. 2.
Fig. 2.

Normalized distributions of detected photon numbers (calculated). The black line shows the distribution for a Poisson process with mean µ = 4.8, i.e. without considering dead time effects. The red graph shows the expected distribution for an (extendable) dead time of the PMT of τd = 2.7 ns and a sampling interval of τs = 20 ns. This results in a strongly modified distribution, now with a mean µr = 2.51 (see text). Lines are guide to the eyes. The inset exhibits the origin of the extendable dead time, where overlapping PMT pulses are not resolved anymore by the threshold electronics.

Fig. 3.
Fig. 3.

Comparison between the dependency of the modulus of the bias of a random bit string on the detected mean photon number for an ideal Poisson process and for a process with extendable dead time. For this plot the dead time was chosen to be τd = 2.7 ns and the sampling frequency to be τs = 20 ns. The inset is a linear plot of the region of interest.

Fig. 4.
Fig. 4.

Measurement of the bias depending on the mean number of detected photons (a). Each data point is obtained from an 8 Gbit bit string for three different sampling times. Serial correlation coefficient SCCl of a single 40 Gbit string, collected with a sampling time of τs = 20 ns and a mean photon number of µr = 1.41, as a function of the bit distance (b). The statistical error levels shown in the plots are the 3-σ variance of the bias b or the SCCl to be expected for an ideal random bit sequence with finite sample length.

Fig. 5.
Fig. 5.

Typical results of the standard statistical test suites STS (a) and Dieharder(b) for a typical sequence of 40 Gbit. Without processing, the p-values are routinely above the significance level confirming the quality and the reliability of the QRNG

Equations (3)

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P ( n , μ ) = μ n n ! e μ .
P ( n , μ r ) = μ r n n ! e μ r · Poisson Σ k = 0 K n ( μ r ) k k ! e μ r · ( ( 1 ( k + n 1 ) τ d τ s ) ) n + k extendable dead time modification ,
b = 1 2 p 1 = 1 2 Σ n = 1 , 3 , . . . P ( n , μ ) .

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