Abstract

We report a quantum random number generator based on the photon-number–path entangled state that is prepared by means of two-photon quantum interference at a beam splitter. The randomness in our scheme is truly quantum mechanical in origin since it results from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.

© 2009 Optical Society of America

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  1. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, “A fast and compact quantum random number generator,” Rev. Sci. Instrum. 71, 1675-1680 (2000).
    [CrossRef]
  2. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47, 595-598 (2000).
  3. P. X. Wang, G. L. Long, and Y. S. Li, “Scheme for a quantum random number generator,” J. Appl. Phys. 100, 056107 (2006).
    [CrossRef]
  4. H.-Q. Ma, Y. Xie, and L.-A. Wu, “Random number generation based on the time of arrival of single photons,” Appl. Opt. 44, 7760-7763 (2005).
    [CrossRef] [PubMed]
  5. M. Stipcevic and B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).
    [CrossRef] [PubMed]
  6. M. A. Wayne, G. Akselrod, E. R. Jeffrey, and P. G. Kwiat, “High-speed quantum random number generation,” in International Conference on Quantum Information (Optical Society of America, 2007). paper JWC49.
  7. H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
    [CrossRef]
  8. M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
    [CrossRef]
  9. C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58-60 (1986).
    [CrossRef] [PubMed]
  10. Implementation of the beam splitter QRNG scheme reported in Ref. makes use of only the signal photon of the SPDC signal-idler photon pair. The scheme, therefore, is equivalent to illuminating a beam splitter with a weak thermal light .
  11. D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685-2688 (1999).
    [CrossRef]
  12. S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).
    [CrossRef]
  13. S. Takeuchi, “Beamlike twin-photon generation by use of type II parametric downconversion,” Opt. Lett. 26, 843-845 (2001).
    [CrossRef]
  14. Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
    [CrossRef]
  15. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987).
    [CrossRef] [PubMed]
  16. Generally speaking, although commonly in use, it is incorrect to say that two photons must simultaneously arrive at a beam splitter to exhibit two-photon quantum interference. The condition for observing two-photon quantum interference involving a beam splitter is that the two biphoton detection amplitudes be indistinguishable. It is in fact possible to observe two-photon quantum interference without actually overlapping two photons at the beam splitter. See Refs. .
  17. T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
    [CrossRef] [PubMed]
  18. Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352-357 (2003).
    [CrossRef]
  19. Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. Am. B 22, 493-498 (2005).
    [CrossRef]
  20. Y.-H. Kim and W. P. Grice, “Observation of correlated-photon statistics using a single detector,” Phys. Rev. A 67, 065802 (2003).
    [CrossRef]
  21. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377-15386 (2007).
    [PubMed]
  22. J. von Neumann, “Various techniques used in connection with random digits,” National Bureau of Standards Applied Mathematics Series No. 12, (National Bureau of Standards, 1951), pp.36-38.
  23. Y. Peres, “Iterating von Neumann's procedure for extracting random bits,” Ann. Stat. 20, 590-597 (1992).
    [CrossRef]
  24. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

2008 (1)

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).
[CrossRef]

2007 (3)

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

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[CrossRef]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377-15386 (2007).
[PubMed]

2006 (1)

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

2005 (2)

2004 (1)

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

2003 (3)

Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[CrossRef]

Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352-357 (2003).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Observation of correlated-photon statistics using a single detector,” Phys. Rev. A 67, 065802 (2003).
[CrossRef]

2001 (1)

2000 (2)

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

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

1999 (1)

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685-2688 (1999).
[CrossRef]

1996 (1)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

1992 (1)

Y. Peres, “Iterating von Neumann's procedure for extracting random bits,” Ann. Stat. 20, 590-597 (1992).
[CrossRef]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

1986 (1)

C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Achleitner, U.

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

Akselrod, G.

M. A. Wayne, G. Akselrod, E. R. Jeffrey, and P. G. Kwiat, “High-speed quantum random number generation,” in International Conference on Quantum Information (Optical Society of America, 2007). paper JWC49.

Baek, S.-Y.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).
[CrossRef]

Banks, D.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Barker, E.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Beausoleil, R. G.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[CrossRef]

Chang, J.-T.

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Dray, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Fedrizzi, A.

Fiorentino, M.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[CrossRef]

Gisin, N.

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

Grice, W. P.

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. Am. B 22, 493-498 (2005).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Observation of correlated-photon statistics using a single detector,” Phys. Rev. A 67, 065802 (2003).
[CrossRef]

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).

Heckert, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Herbst, T.

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Hou, Y.-X.

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Jeffrey, E. R.

M. A. Wayne, G. Akselrod, E. R. Jeffrey, and P. G. Kwiat, “High-speed quantum random number generation,” in International Conference on Quantum Information (Optical Society of America, 2007). paper JWC49.

Jennewein, T.

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377-15386 (2007).
[PubMed]

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

Ji, L.-L.

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Kim, Y.-H.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Quantum interference with distinguishable photons through indistinguishable pathways,” J. Opt. Soc. Am. B 22, 493-498 (2005).
[CrossRef]

Y.-H. Kim, “Two-photon interference without bunching two photons,” Phys. Lett. A 315, 352-357 (2003).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Observation of correlated-photon statistics using a single detector,” Phys. Rev. A 67, 065802 (2003).
[CrossRef]

Y.-H. Kim, “Quantum interference with beamlike type-II spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[CrossRef]

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685-2688 (1999).
[CrossRef]

Kwiat, P. G.

M. A. Wayne, G. Akselrod, E. R. Jeffrey, and P. G. Kwiat, “High-speed quantum random number generation,” in International Conference on Quantum Information (Optical Society of America, 2007). paper JWC49.

Kwon, O.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, “Temporal shaping of a heralded single-photon wave packet,” Phys. Rev. A 77, 013829 (2008).
[CrossRef]

Leigh, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Levenson, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Li, Y. S.

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

Long, G. L.

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

Ma, H.-Q.

H.-Q. Ma, Y. Xie, and L.-A. Wu, “Random number generation based on the time of arrival of single photons,” Appl. Opt. 44, 7760-7763 (2005).
[CrossRef] [PubMed]

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, “Experimental realization of a localized one-photon state,” Phys. Rev. Lett. 56, 58-60 (1986).
[CrossRef] [PubMed]

Migdall, A.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Munro, W. G.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[CrossRef]

Nechvatal, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Peres, Y.

Y. Peres, “Iterating von Neumann's procedure for extracting random bits,” Ann. Stat. 20, 590-597 (1992).
[CrossRef]

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Poppe, A.

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]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Rukhin, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Santori, C.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Shih, Y.

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685-2688 (1999).
[CrossRef]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Smid, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Soto, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Spillane, S. M.

M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, “Secure self-calibrating quantum random-bit generator,” Phys. Rev. A 75, 032334 (2007).
[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).

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]

Strekalov, D. V.

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685-2688 (1999).
[CrossRef]

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two photons?,” Phys. Rev. Lett. 77, 1917-1920 (1996).
[CrossRef] [PubMed]

Takeuchi, S.

Vangel, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

Vo, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 (NIST, 2008), http://csrc.nist.gov/rng/.

von Neumann, J.

J. von Neumann, “Various techniques used in connection with random digits,” National Bureau of Standards Applied Mathematics Series No. 12, (National Bureau of Standards, 1951), pp.36-38.

Wang, P. X.

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

Wang, S.-M.

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Wayne, M. A.

M. A. Wayne, G. Akselrod, E. R. Jeffrey, and P. G. Kwiat, “High-speed quantum random number generation,” in International Conference on Quantum Information (Optical Society of America, 2007). paper JWC49.

Weihs, G.

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

Weinfurter, H.

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

Wu, L.-A.

H.-Q. Ma, Y. Xie, and L.-A. Wu, “Random number generation based on the time of arrival of single photons,” Appl. Opt. 44, 7760-7763 (2005).
[CrossRef] [PubMed]

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Xie, Y.

Zbinden, H.

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

Zeilinger, A.

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377-15386 (2007).
[PubMed]

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

Zhang, D.

H.-Q. Ma, S.-M. Wang, D. Zhang, J.-T. Chang, L.-L. Ji, Y.-X. Hou, and L.-A. Wu, “A random number generator based on quantum entangled photon pairs,” Chin. Phys. Lett. 21, 1961-1965 (2004).
[CrossRef]

Ann. Stat. (1)

Y. Peres, “Iterating von Neumann's procedure for extracting random bits,” Ann. Stat. 20, 590-597 (1992).
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Implementation of the beam splitter QRNG scheme reported in Ref. makes use of only the signal photon of the SPDC signal-idler photon pair. The scheme, therefore, is equivalent to illuminating a beam splitter with a weak thermal light .

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Generally speaking, although commonly in use, it is incorrect to say that two photons must simultaneously arrive at a beam splitter to exhibit two-photon quantum interference. The condition for observing two-photon quantum interference involving a beam splitter is that the two biphoton detection amplitudes be indistinguishable. It is in fact possible to observe two-photon quantum interference without actually overlapping two photons at the beam splitter. See Refs. .

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experiment. The two-photon photon-number–path entangled state is prepared by interfering the SPDC photon pair at a FBS. The coincidence events between detectors D1–D2 and D3–D4 form bit value 0 and bit value 1, respectively.

Fig. 2
Fig. 2

(a) Coincidence between two detectors placed at the end of the first FBS. The solid curve represents a Gaussian fit to the data and the resulting visibility is 100 ± 0.0168 % . The D1–D3 coincidence shows a dip with the same visibility. (b) D1–D2 coincidence and (c) D3–D4 coincidence exhibit peaks at the delay where the dip occurs.

Fig. 3
Fig. 3

Bit sequence generation scheme. D1–D2 coincidence and D3–D4 coincidence occur randomly because of the entangled state in Eq. (1). If there is a D1–D2 or D3–D4 coincidence event between two successive counting clock pulses, we record a bit value of 0 or 1, respectively. If there are two or more such events within the time period, we record that as an error. The error bit can be removed by increasing the counting clock frequency.

Fig. 4
Fig. 4

BER versus the counting clock frequency. The solid curve represents Eq. (2) with R B = 668 Hz . The filled circles represent the experimental data with one standard deviation error bar.

Tables (1)

Tables Icon

Table 1 Results (P Values) of the Statistical Randomness Test Obtained with the NIST STS [24] a

Equations (4)

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

| ψ = | 2 3 | 0 4 + | 0 3 | 2 4 2 ,
BER = R B 2 f .
| ψ = | 0 + η | 1 1 | 1 2 + η 2 | 2 1 | 2 2 + ,
6 4 ( | 4 3 | 0 4 + | 0 3 | 4 4 ) + | 2 3 | 2 4 2 .

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