Abstract

We propose and demonstrate a technique for quantum random number generation based on the random population of the output spatial modes of a beam splitter when both inputs are simultaneously fed with indistinguishable weak coherent states. We simulate and experimentally validate the probability of generation of random bits as a function of the average photon number per input, and compare it to the traditional approach of a single weak coherent state transmitted through a beam-splitter, showing an improvement of up to 32%. The ensuing interference phenomenon reduces the probability of coincident counts between the detectors associated with bits 0 and 1, thus increasing the probability of occurrence of a valid output. A long bit string is assessed by a standard randomness test suite with good confidence. Our proposal can be easily implemented and opens attractive performance gains without a significant trade-off.

© 2016 Optical Society of America

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References

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  1. N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
    [Crossref] [PubMed]
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [Crossref]
  3. http://www.mathworks.com/products/matlab/
  4. M. Herrero-Collantes and J. C. Garcia-Escartin, “Quantum random number generators,” arXiv:1604.03304v1, 2016.
  5. J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
    [Crossref]
  6. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Modern Optics 47, 595–598, 2000.
  7. 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]
  8. 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 (2004).
    [Crossref]
  9. O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
    [Crossref]
  10. Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, 2007).
  11. 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]
  12. H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209 (1986).
    [Crossref]
  13. Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
    [Crossref]
  14. T. Ferreira da Silva, G. C. do Amaral, D. Vitoreti, G. P. Temporão, and J. P. von der Weid, “Spectral characterization of weak coherent state sources based on two-photon interference,” J. Opt. Soc. Am. B 32, 545–549 (2015).
    [Crossref]
  15. G. C. Amaral, T. Ferreira da Silva, G. P. Temporão, and J. P. von der Weid, “Few-photon heteorodyne spectroscopy,” Opt. Lett. 41, 1502–1505 (2016).
    [Crossref] [PubMed]
  16. X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
    [Crossref]
  17. T. Ferreira da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
    [Crossref]
  18. Y. Peres, “Iterating von Neumann’s procedure for extracting random bits,” Ann. Stat. 20, 590–597 (1992).
    [Crossref]
  19. 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.

2016 (1)

2015 (1)

2013 (1)

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

2011 (1)

T. Ferreira da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

2009 (1)

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
[Crossref]

2005 (1)

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

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 (2004).
[Crossref]

2002 (1)

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

2000 (2)

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

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]

1994 (1)

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[Crossref]

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)

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209 (1986).
[Crossref]

1949 (1)

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

Amaral, G. C.

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.

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.

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 (2004).
[Crossref]

Cho, Y.-W.

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
[Crossref]

do Amaral, G. C.

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.

Ferreira da Silva, T.

Garcia-Escartin, J. C.

M. Herrero-Collantes and J. C. Garcia-Escartin, “Quantum random number generators,” arXiv:1604.03304v1, 2016.

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. Modern Optics 47, 595–598, 2000.

Guinnard, L.

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

Guinnard, O.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Modern Optics 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.

Herrero-Collantes, M.

M. Herrero-Collantes and J. C. Garcia-Escartin, “Quantum random number generators,” arXiv:1604.03304v1, 2016.

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]

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 (2004).
[Crossref]

Jennewein, T.

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 (2004).
[Crossref]

Kim, Y.-H.

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
[Crossref]

Kim, Y.-S.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

Kuo, P. S.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

Kwon, O.

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
[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.

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.

Lo, H.-K.

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Ma, H.-Q.

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 (2004).
[Crossref]

Ma, X.

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[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]

Metropolis, N.

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

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.

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]

Ou, Z.-Y. J.

Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, 2007).

Owens, P.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[Crossref]

Paul, H.

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209 (1986).
[Crossref]

Peres, Y.

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

Qi, B.

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Rarity, J.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[Crossref]

Ribordy, G.

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

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.

Slattery, O.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

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.

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.

Stefanov, A.

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

Tang, X.

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

Tapster, P.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[Crossref]

Temporão, G. P.

Tittel, W.

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

Ulam, S.

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

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.

Vitoreti, D.

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.

von der Weid, J. P.

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 (2004).
[Crossref]

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, 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 (2004).
[Crossref]

Xavier, G. B.

T. Ferreira da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[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. Modern Optics 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. 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 (2004).
[Crossref]

Zhao, Z.

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Ann. Stat. (1)

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

App. Opt. (1)

O. Kwon, Y.-W. Cho, and Y.-H. Kim, “Quantum random number generator using photon-number path entanglement,” App. Opt. 48, 1774–1778 (2009).
[Crossref]

Chin. Phys. Lett. (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 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Ferreira da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[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. Mod. Opt. (1)

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
[Crossref]

J. Modern Optics (1)

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Rev. A (2)

X. Ma, B. Qi, Z. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Y.-S. Kim, O. Slattery, P. S. Kuo, and X. Tang, “Conditions for two-photon interference with coherent pulses”, Phys. Rev. A 87, 063843 (2013).
[Crossref]

Phys. Rev. Lett. (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]

Rev. Mod. Phys. (2)

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209 (1986).
[Crossref]

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

Rev. Sci. Instrum. (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]

Other (4)

Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, 2007).

http://www.mathworks.com/products/matlab/

M. Herrero-Collantes and J. C. Garcia-Escartin, “Quantum random number generators,” arXiv:1604.03304v1, 2016.

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.

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Figures (3)

Fig. 1
Fig. 1 QRNG based on random path-splitting enhanced by interference of indistinguishable WCSs. The experimental setup of the optical source is detailed in the inset on the left. The inset on the right shows the sampled channels: (−) represents no output bit generated when both SPDs click, while a single-channel detection is associated to bit 0 or 1. LD: laser diode; VOA: variable optical attenuator; BS: beam splitter; OD: optical delay; PC: polarization controller; PU: processing unit.
Fig. 2
Fig. 2 Probability of generation of a valid output bit (Pgen) and probability of discard due to collision (Pdisc) by inputting single WCS plus vacuum or indistinguishable WCSs into the BS. Points are measured data and lines are obtained by numerical simulation.
Fig. 3
Fig. 3 Results of the randomness test suite for the generated random bit sequence using indistinguishable WCSs.

Equations (5)

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

ρ a , b = [ 0 2 π | μ e j θ μ e j θ | d θ ] 2
P a , b ( m , n ) = e μ μ m + n / ( m ! n ! 2 m , n )
| ψ c , d = u = 0 m v = 0 n j u + v m ! n ! ( m u + v ) ! ( n v + u ) ! 2 ( m + n ) / 2 ( m u ) ! u ! ( n v ) ! v ! | m u + v , n v + u c , d
P c , d ( M , N ) = m = 0 n = 0 P a , b ( m , n ) ψ | M , N c , d
P g e n = M = 1 P c , d ( M , 0 ) η M + M = 1 N = 1 P c , d ( M , N ) η M ( 1 η N ) + N = 1 P c , d ( 0 , N ) η N + M = 1 N = 1 P c , d ( M , N ) ( 1 η M ) η N P d i s c = M = 1 N = 1 P c , d ( M , N ) η M η N

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