Abstract

We present a random number generation scheme based on measuring the phase fluctuations of a laser with a simple experimental setup. A simple model is established to analyze the randomness and the simulation result based on this model fits well with the experiment data. After the analog to digital sampling and suitable randomness extraction integrated in the field programmable gate array, the final random bits are delivered to a PC, realizing a 5.4 Gbps real time quantum random number generation. The final random bit sequences have passed all the NIST and DIEHARD tests.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2016 (3)

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

Z. Cao, H. Zhou, X. Yuan, and X. Ma, “Source-independent quantum random number generation,” Phys. Rev. X 6(1), 011020 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

2015 (4)

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

H. Zhou, X. Yuan, and X. Ma, “Randomness generation based on spontaneous emissions of lasers,” Phys. Rev. A 91(6), 062316 (2015).
[Crossref]

A. Martin, B. Sanguinetti, C. C. W. Lim, R. Houlmann, and H. Zbinden, “Quantum random number generation for 1.25-GHz quantum key distribution systems,” J. Lightwave Technol. 33(13), 2855–2859 (2015).
[Crossref]

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

2012 (3)

J. Bouda, M. Pivoluska, M. Plesch, and C. Wilmott, “Weak randomness seriously limits the security of quantum key distribution,” Phys. Rev. A 86(6), 062308 (2012).
[Crossref]

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE Photonics Technol. Lett. 24(6), 437–439 (2012).
[Crossref]

F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20(11), 12366–12377 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (3)

2005 (1)

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

2000 (2)

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 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(4), 1675–1680 (2000).
[Crossref]

1994 (1)

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

1983 (1)

K. Vahala and A. Yariv, “Occupation fluctuation noise: A fundamental source of linewidth broadening in semiconductor lasers,” Appl. Phys. Lett. 43(2), 140 (1983).
[Crossref]

1982 (1)

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

1949 (1)

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 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(4), 1675–1680 (2000).
[Crossref]

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Anzolin, G.

Bouda, J.

J. Bouda, M. Pivoluska, M. Plesch, and C. Wilmott, “Weak randomness seriously limits the security of quantum key distribution,” Phys. Rev. A 86(6), 062308 (2012).
[Crossref]

Cao, Z.

Z. Cao, H. Zhou, X. Yuan, and X. Ma, “Source-independent quantum random number generation,” Phys. Rev. X 6(1), 011020 (2016).
[Crossref]

Chen, W.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Chi, Y.-M.

Cohen, A. B.

Curty, M.

Dang, A.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE Photonics Technol. Lett. 24(6), 437–439 (2012).
[Crossref]

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Guinnard, L.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 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(4), 595–598 (2000).

Guo, G.-C.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Guo, H.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE Photonics Technol. Lett. 24(6), 437–439 (2012).
[Crossref]

Guo, X.

Guo, Y.

Han, Z.-F.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Henry, C.

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Houlmann, R.

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(4), 1675–1680 (2000).
[Crossref]

Jofre, M.

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Li, H.-W.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Li, P.

Li, X.

Liang, H.

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Lim, C. C. W.

Liu, X.

Lo, H.-K.

Ma, H. Q.

Ma, X.

Z. Cao, H. Zhou, X. Yuan, and X. Ma, “Source-independent quantum random number generation,” Phys. Rev. X 6(1), 011020 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

H. Zhou, X. Yuan, and X. Ma, “Randomness generation based on spontaneous emissions of lasers,” Phys. Rev. A 91(6), 062316 (2015).
[Crossref]

F. Xu, B. Qi, X. Ma, H. Xu, H. Zheng, and H.-K. Lo, “Ultrafast quantum random number generation based on quantum phase fluctuations,” Opt. Express 20(11), 12366–12377 (2012).
[Crossref] [PubMed]

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Martin, A.

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[Crossref] [PubMed]

Mitchell, M. W.

Murphy, T. E.

Nie, Y. Q.

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Owens, P.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Pan, J. W.

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Pivoluska, M.

J. Bouda, M. Pivoluska, M. Plesch, and C. Wilmott, “Weak randomness seriously limits the security of quantum key distribution,” Phys. Rev. A 86(6), 062308 (2012).
[Crossref]

Plesch, M.

J. Bouda, M. Pivoluska, M. Plesch, and C. Wilmott, “Weak randomness seriously limits the security of quantum key distribution,” Phys. Rev. A 86(6), 062308 (2012).
[Crossref]

Pruneri, V.

Qi, B.

Qian, L.

Qian, Y.-J.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Rarity, J.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Roy, R.

Sanguinetti, B.

Stefanov, A.

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 595–598 (2000).

Steinlechner, F.

Sun, Y.

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Tapster, P.

J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41(12), 2435–2444 (1994).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Torres, J. P.

Ulam, S.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44(247), 335–341 (1949).
[Crossref] [PubMed]

Vahala, K.

K. Vahala and A. Yariv, “Occupation fluctuation noise: A fundamental source of linewidth broadening in semiconductor lasers,” Appl. Phys. Lett. 43(2), 140 (1983).
[Crossref]

Wang, S.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Wang, Y.

Wang, Y. C.

Wei, W.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE Photonics Technol. Lett. 24(6), 437–439 (2012).
[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(4), 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(4), 1675–1680 (2000).
[Crossref]

Wilmott, C.

J. Bouda, M. Pivoluska, M. Plesch, and C. Wilmott, “Weak randomness seriously limits the security of quantum key distribution,” Phys. Rev. A 86(6), 062308 (2012).
[Crossref]

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[Crossref]

Wu, L. A.

Xie, G.

W. Wei, G. Xie, A. Dang, and H. Guo, “High-speed and bias-free optical random number generator,” IEEE Photonics Technol. Lett. 24(6), 437–439 (2012).
[Crossref]

Xie, Y.

Xu, F.

Xu, H.

Yariv, A.

K. Vahala and A. Yariv, “Occupation fluctuation noise: A fundamental source of linewidth broadening in semiconductor lasers,” Appl. Phys. Lett. 43(2), 140 (1983).
[Crossref]

Yi, X.

Yin, Z.-Q.

H.-W. Li, Z.-Q. Yin, S. Wang, Y.-J. Qian, W. Chen, G.-C. Guo, and Z.-F. Han, “Randomness determines practical security of BB84 quantum key distribution,” Sci. Rep. 5, 16200 (2015).
[Crossref] [PubMed]

Yuan, X.

Z. Cao, H. Zhou, X. Yuan, and X. Ma, “Source-independent quantum random number generation,” Phys. Rev. X 6(1), 011020 (2016).
[Crossref]

H. Zhou, X. Yuan, and X. Ma, “Randomness generation based on spontaneous emissions of lasers,” Phys. Rev. A 91(6), 062316 (2015).
[Crossref]

Zbinden, H.

A. Martin, B. Sanguinetti, C. C. W. Lim, R. Houlmann, and H. Zbinden, “Quantum random number generation for 1.25-GHz quantum key distribution systems,” J. Lightwave Technol. 33(13), 2855–2859 (2015).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, “Optical quantum random number generator,” J. Mod. Opt. 47(4), 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(4), 1675–1680 (2000).
[Crossref]

Zhang, J.

P. Li, Y. Sun, X. Liu, X. Yi, J. Zhang, X. Guo, Y. Guo, and Y. Wang, “Fully photonics-based physical random bit generator,” Opt. Lett. 41(14), 3347–3350 (2016).
[Crossref] [PubMed]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “68 Gbps quantum random number generation by measuring laser phase fluctuations,” Rev. Sci. Instrum. 86(6), 063105 (2015).
[Crossref] [PubMed]

Zhang, J. Z.

Zhang, X. G.

X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

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Zheng, H.

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X. G. Zhang, Y. Q. Nie, H. Zhou, H. Liang, X. Ma, J. Zhang, and J. W. Pan, “Fully integrated 3.2Gbps quantum random number generator with real-time extraction,” Rev. Sci. Instrum. 87(7), 076102 (2016).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 The Experimental setup of the proposed QRNG. The CW beams emitted by the laser diode enter one input port (port 1) of the BS. Then half of the beams are directly coupled into the PD and another half of the beams are coupled into the delay loop, which consists of the BS and a 4m DL. Every circulation of the delay loop introduces a time delay of 20 ns. The beams from port 2 will interfere with the beams from the laser diode at the BS. The output from the PD can be either acquired by a DSO to analyze the distribution of the raw data or be processed by an ADC and a randomness-extractor to distill the final random bits. CW: continuous wave, BS: 2 × 2 50/50 polarization-maintaining beam splitter, DL: delay line, PD: photo-detector with high bandwidth, DSO: digital storage oscilloscope, ADC: 12-bit analog-to-digital converter.
Fig. 2
Fig. 2 The normalized distribution of the simulation result of the theoretical model for the proposed QRNG and the experimental measured interference intensity.
Fig. 3
Fig. 3 Noise spectra. The spectral density of total phase fluctuation (blue), intensity noise (red), and background noise (black).
Fig. 4
Fig. 4 Normalized min entropy H min ( l )/l of 10 7 extracted random bits after XOR operation and m-LSB procedure, m=2,4,6,8 .
Fig. 5
Fig. 5 Autocorrelation analysis of 10 7 extracted random bits after XOR operation and 6-LSB procedure within 100 bit-delay. The average value is 1.68× 10 5 .
Fig. 6
Fig. 6 Results of the NIST-STS test suite for a 1Gbit sequence. The significance was set by 0.01. To pass the test, p-value needs to satisfy 0.01pvalue0.99 .
Fig. 7
Fig. 7 Results of the Diehard statistical suite for a 1Gbit sequence. For the case of multiple p-values in Diehard test suite, a Kolmogorov- Smirnov (KS) test is used to obtain a final p-value, which measures the uniformity of the multiple p-value.

Equations (3)

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E p1 ( t )=Aexp[ iωt+iφ( t ) ]
E p2 ( t )=A k=1 N ( β 2 ) k 2 exp[ iω( tkΔt )+iφ( tkΔt ) ]
I= 1 2 A 2 k=0 N ( β 2 ) k + A 2 k=1 N ( β 2 ) k 2 ( cos( kωΔt+Δ φ N k ) ) + A 2 k=1 N ( β 2 ) k 2 ( j=1 k1 ( β 2 ) j 2 cos[ ( kj )ωΔt+Δ φ Nj kj ] )

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