S. Scheel, “Single-photon sources—an introduction,” J. Mod. Opt. 56, 141–160 (2009).

[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (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]

M. Stipcevid and B. Medved Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).

[CrossRef]

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, 1961–1964 (2004).

[CrossRef]

A. Galindo and M. A. Martín-Delgado, “Information and computation: classical and quantum aspects,” Rev. Mod. Phys. 74, 347–423 (2002).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

M. P. Silverman and W. Strange, “Experimental tests for randomness of quantum decay examined as a Markov process,” Phys. Lett. A 272, 1–9 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (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).

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).

[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).

[CrossRef]

A. Steane, “Quantum computing,” Rep. Prog. Phys. 61, 117–173 (1998).

[CrossRef]

T. Erber, “Testing the randomness of quantum mechanics: nature’s ultimate cryptogram?” Ann. N.Y. Acad. Sci. 755, 748–756 (1995).

[CrossRef]

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).

[CrossRef]

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

[CrossRef]
[PubMed]

D. C. Burnham and D. L. Weinberg, “Observation of simutaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).

[CrossRef]

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

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).

[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).

[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).

[CrossRef]

D. C. Burnham and D. L. Weinberg, “Observation of simutaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).

[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

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, 1961–1964 (2004).

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (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]

T. Erber, “Testing the randomness of quantum mechanics: nature’s ultimate cryptogram?” Ann. N.Y. Acad. Sci. 755, 748–756 (1995).

[CrossRef]

A. Galindo and M. A. Martín-Delgado, “Information and computation: classical and quantum aspects,” Rev. Mod. Phys. 74, 347–423 (2002).

[CrossRef]

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).

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

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

S.-J. Kim, K. Umeno, and A. Hasegawa, On the NIST Statistical Test Suite for RandomnessIEICE Tech. Rep. (IEICE, 2003) Vol. 103, 21–27.

S.-J. Kim, K. Umeno, and A. Hasegawa, Corrections of the NIST Statistical Test Suite for Randomness Report 2004/018 (Cryptology ePrint Archive, 2004).

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

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

[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, 1961–1964 (2004).

[CrossRef]

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

[CrossRef]

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, 1961–1964 (2004).

[CrossRef]

S.-J. Kim, K. Umeno, and A. Hasegawa, Corrections of the NIST Statistical Test Suite for Randomness Report 2004/018 (Cryptology ePrint Archive, 2004).

S.-J. Kim, K. Umeno, and A. Hasegawa, On the NIST Statistical Test Suite for RandomnessIEICE Tech. Rep. (IEICE, 2003) Vol. 103, 21–27.

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

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, 1961–1964 (2004).

[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).

[CrossRef]

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

[CrossRef]
[PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

A. Galindo and M. A. Martín-Delgado, “Information and computation: classical and quantum aspects,” Rev. Mod. Phys. 74, 347–423 (2002).

[CrossRef]

M. Stipcevid and B. Medved Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).

[CrossRef]

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

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

S. Scheel, “Single-photon sources—an introduction,” J. Mod. Opt. 56, 141–160 (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]

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. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

M. P. Silverman and W. Strange, “Experimental tests for randomness of quantum decay examined as a Markov process,” Phys. Lett. A 272, 1–9 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

A. Steane, “Quantum computing,” Rep. Prog. Phys. 61, 117–173 (1998).

[CrossRef]

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

M. Stipcevid and B. Medved Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (2000).

[CrossRef]

M. P. Silverman and W. Strange, “Experimental tests for randomness of quantum decay examined as a Markov process,” Phys. Lett. A 272, 1–9 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

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

[CrossRef]

S.-J. Kim, K. Umeno, and A. Hasegawa, On the NIST Statistical Test Suite for RandomnessIEICE Tech. Rep. (IEICE, 2003) Vol. 103, 21–27.

S.-J. Kim, K. Umeno, and A. Hasegawa, Corrections of the NIST Statistical Test Suite for Randomness Report 2004/018 (Cryptology ePrint Archive, 2004).

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

J. Von Neumann, “Various techniques used in connection with random digits,” Nat. Bur. Stand. (U. S.) Appl. Math Series No. 12 (GPO, 1951) pp. 36–38.

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, 1961–1964 (2004).

[CrossRef]

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

[CrossRef]

D. C. Burnham and D. L. Weinberg, “Observation of simutaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).

[CrossRef]

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

[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

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, 1961–1964 (2004).

[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]

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).

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

[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).

[CrossRef]

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, 1961–1964 (2004).

[CrossRef]

D. Branning, S. Bhandari, and M. Beck, “Low-cost coincidence-counting electronics for undergraduate quantum optics,” Am. J. Phys. 77, 667–670 (2009).

[CrossRef]

T. Erber, “Testing the randomness of quantum mechanics: nature’s ultimate cryptogram?” Ann. N.Y. Acad. Sci. 755, 748–756 (1995).

[CrossRef]

Y. Peres, “Iterating Von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).

[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]

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, 1961–1964 (2004).

[CrossRef]

S. Scheel, “Single-photon sources—an introduction,” J. Mod. Opt. 56, 141–160 (2009).

[CrossRef]

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

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests of alpha-, beta-, and electron capture decays for randomness,” Phys. Lett. A 262, 265–273 (1999).

[CrossRef]

M. P. Silverman and W. Strange, “Experimental tests for randomness of quantum decay examined as a Markov process,” Phys. Lett. A 272, 1–9 (2000).

[CrossRef]

M. P. Silverman, W. Strange, C. R. Silverman, and T. C. Lipscombe, “Tests for randomness of spontaneous quantum decay,” Phys. Rev. A 61, 042106 (2000).

[CrossRef]

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

[CrossRef]
[PubMed]

D. C. Burnham and D. L. Weinberg, “Observation of simutaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).

[CrossRef]

A. Steane, “Quantum computing,” Rep. Prog. Phys. 61, 117–173 (1998).

[CrossRef]

A. Galindo and M. A. Martín-Delgado, “Information and computation: classical and quantum aspects,” Rev. Mod. Phys. 74, 347–423 (2002).

[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).

[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288–S297 (1999).

[CrossRef]

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

[CrossRef]

V. Scarani, H. Bechmann-Pasquinucci, N. Cerf, M. Dusek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).

[CrossRef]

M. Stipcevid and B. Medved Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78, 045104 (2007).

[CrossRef]

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

[CrossRef]

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 (revised),” Natl. Inst. Stand. Technol. (U. S.) Spec. Publ. 800-22rev1 (2008) http://csrc. nist. gov/groups/ST/toolkit/rng/documentation_software. html.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

There is an error in the current NIST publication concerning this test: in section , although all of the formulae appear to be correct, the last three tables of probabilities (for M=512, 1000, and 10000) are not. The source code for the Statistical Test Suite provided by NIST, to the extent that it makes use of these incorrect probabilities, is also in error.

S.-J. Kim, K. Umeno, and A. Hasegawa, On the NIST Statistical Test Suite for RandomnessIEICE Tech. Rep. (IEICE, 2003) Vol. 103, 21–27.

S.-J. Kim, K. Umeno, and A. Hasegawa, Corrections of the NIST Statistical Test Suite for Randomness Report 2004/018 (Cryptology ePrint Archive, 2004).

The current NIST publication also contains an error regarding this test: on page 2–32, Eq. , the absolute value of Sk should be divided by n.

J. Von Neumann, “Various techniques used in connection with random digits,” Nat. Bur. Stand. (U. S.) Appl. Math Series No. 12 (GPO, 1951) pp. 36–38.