Abstract

We report the interferometric photodetection of a phase-diffusion quantum entropy source in a silicon photonics chip. The device uses efficient and robust single-laser accelerated phase diffusion methods, and implements the unbalanced Mach-Zehnder interferometer with optimized splitting ratio and photodetection, in a 0.5 mm×1 mm footprint. We demonstrate Gbps raw entropy-generation rates in a technology compatible with conventional CMOS fabrication techniques.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip

Francesco Raffaelli, Philip Sibson, Jake E. Kennard, Dylan H. Mahler, Mark G. Thompson, and Jonathan C. F. Matthews
Opt. Express 26(16) 19730-19741 (2018)

Quantum entropy source on an InP photonic integrated circuit for random number generation

Carlos Abellan, Waldimar Amaya, David Domenech, Pascual Muñoz, Jose Capmany, Stefano Longhi, Morgan W. Mitchell, and Valerio Pruneri
Optica 3(9) 989-994 (2016)

Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell
Opt. Express 22(2) 1645-1654 (2014)

References

  • View by:
  • |
  • |
  • |

  1. X. Cai and X. Wang, “Stochastic modeling and simulation of gene networks-a review of the state-of-the-art research on stochastic simulations,” IEEE Signal Process. Mag. 24, 27–36 (2007).
    [Crossref]
  2. T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
    [Crossref]
  3. C. Hall and B. Schneier, “Remote electronic gambling,” in Proceedings 13th Annual Computer Security Applications Conference, (1997), pp. 232–238.
    [Crossref]
  4. C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
    [Crossref]
  5. A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
    [Crossref]
  6. C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
    [Crossref]
  7. B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
    [Crossref] [PubMed]
  8. M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
    [Crossref]
  9. L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
    [Crossref]
  10. J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Ser. 12, 36–38 (1951).
  11. J. Rarity, P. Owens, and P. Tapster, “Quantum random-number generation and key sharing,” J. Mod. Opt. 41, 2435–2444 (1994).
    [Crossref]
  12. 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]
  13. M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
    [Crossref]
  14. 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. Photon. 4, 711–715 (2010).
    [Crossref]
  15. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
    [Crossref] [PubMed]
  16. K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama, K. Yoshimura, and M. Inubushi, “Real-time fast physical random number generator with a photonic integrated circuit,” Opt. Express 25, 6511–6523 (2017).
    [Crossref] [PubMed]
  17. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010).
    [Crossref] [PubMed]
  18. M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express 19, 20665–20672 (2011).
    [Crossref] [PubMed]
  19. C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
    [Crossref] [PubMed]
  20. Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
    [Crossref]
  21. Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
    [Crossref]
  22. F. Raffaelli, P. Sibson, J. E. Kennard, D. H. Mahler, M. G. Thompson, and J. C. F. Matthews, “Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip,” Opt. Express 26, 19730–19741 (2018).
    [Crossref]
  23. A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
    [Crossref]
  24. C. Abellán, W. Amaya, D. Domenech, P. Muñoz, J. Capmany, S. Longhi, M. W. Mitchell, and V. Pruneri, “Quantum entropy source on an inp photonic integrated circuit for random number generation,” Optica 3, 989–994 (2016).
    [Crossref]
  25. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. photonics 4, 511 (2010).
    [Crossref]
  26. M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
    [Crossref]

2018 (1)

2017 (1)

2016 (1)

2015 (7)

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
[Crossref]

2014 (2)

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
[Crossref] [PubMed]

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

2011 (3)

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express 19, 20665–20672 (2011).
[Crossref] [PubMed]

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
[Crossref]

2010 (4)

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. Photon. 4, 711–715 (2010).
[Crossref]

B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010).
[Crossref] [PubMed]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
[Crossref] [PubMed]

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. photonics 4, 511 (2010).
[Crossref]

2007 (2)

X. Cai and X. Wang, “Stochastic modeling and simulation of gene networks-a review of the state-of-the-art research on stochastic simulations,” IEEE Signal Process. Mag. 24, 27–36 (2007).
[Crossref]

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

2000 (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]

1994 (1)

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

1951 (1)

J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Ser. 12, 36–38 (1951).

1949 (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

Abellan, C.

M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
[Crossref]

Abellán, C.

C. Abellán, W. Amaya, D. Domenech, P. Muñoz, J. Capmany, S. Longhi, M. W. Mitchell, and V. Pruneri, “Quantum entropy source on an inp photonic integrated circuit for random number generation,” Optica 3, 989–994 (2016).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
[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. Instr. 71, 1675–1680 (2000).
[Crossref]

Acín, A.

Allman, M. S.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Amaya, W.

C. Abellán, W. Amaya, D. Domenech, P. Muñoz, J. Capmany, S. Longhi, M. W. Mitchell, and V. Pruneri, “Quantum entropy source on an inp photonic integrated circuit for random number generation,” Optica 3, 989–994 (2016).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
[Crossref]

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
[Crossref] [PubMed]

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. Photon. 4, 711–715 (2010).
[Crossref]

Anzolin, G.

Argyris, A.

Benson, O.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

Berlin, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

Bernien, H.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Beyer, J.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Bienfang, J. C.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Bierhorst, P.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Blok, M. S.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Bogris, A.

Bowers, J. E.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. photonics 4, 511 (2010).
[Crossref]

Cai, X.

X. Cai and X. Wang, “Stochastic modeling and simulation of gene networks-a review of the state-of-the-art research on stochastic simulations,” IEEE Signal Process. Mag. 24, 27–36 (2007).
[Crossref]

Capmany, J.

Chi, Y.-M.

Christensen, B. G.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Click, T. H.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
[Crossref]

Coakley, K. J.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Curty, M.

Deligiannidis, S.

Domenech, D.

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. Photon. 4, 711–715 (2010).
[Crossref]

Dréau, A. E.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Dyer, S. D.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Dynes, J.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Elkouss, D.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Enne, R.

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

Farr, W. H.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Fröhlich, B.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[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. Photon. 4, 711–715 (2010).
[Crossref]

Gerrits, T.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Giustina, M.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Glancy, S.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Hall, C.

C. Hall and B. Schneier, “Remote electronic gambling,” in Proceedings 13th Annual Computer Security Applications Conference, (1997), pp. 232–238.
[Crossref]

Hamel, D. R.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Handsteiner, J.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Hanson, R.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Harayama, T.

Hensen, B.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Hochrainer, A.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Hodge, C.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Hofbauer, M.

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

Huang, L.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Inubushi, M.

Iwakawa, K.

Jennewein, T.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[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]

Jofre, M.

Kalb, N.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Kaminski, G. A.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
[Crossref]

Kennard, J. E.

Khanmohammadi, A.

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

Knill, E.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Kofler, J.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Kumor, D. R.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Kwiat, P. G.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Lambrocco, C.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Larsson, J.-A.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Leifgen, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

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. Photon. 4, 711–715 (2010).
[Crossref]

Liang, D.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. photonics 4, 511 (2010).
[Crossref]

Lita, A. E.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Liu, A.

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
[Crossref]

Liu, Y.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Lo, H.-K.

Longhi, S.

Lucamarini, M.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Maeda, W.

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

Mahler, D. H.

Markham, M.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[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. Photon. 4, 711–715 (2010).
[Crossref]

Marsili, F.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Matthews, J. C. F.

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. Photon. 4, 711–715 (2010).
[Crossref]

Meyer-Scott, E.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Migdall, A. L.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Mirin, R. P.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Mitchell, M. W.

C. Abellán, W. Amaya, D. Domenech, P. Muñoz, J. Capmany, S. Longhi, M. W. Mitchell, and V. Pruneri, “Quantum entropy source on an inp photonic integrated circuit for random number generation,” Optica 3, 989–994 (2016).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
[Crossref] [PubMed]

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express 19, 20665–20672 (2011).
[Crossref] [PubMed]

Mitrani, D.

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

Muñoz, P.

Nam, S. W.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Nie, Y.-Q.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Owens, P.

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

Pan, J.-W.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Payne, F.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Phelan, K.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Pikasis, E.

Plews, A.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Pruneri, V.

C. Abellán, W. Amaya, D. Domenech, P. Muñoz, J. Capmany, S. Longhi, M. W. Mitchell, and V. Pruneri, “Quantum entropy source on an inp photonic integrated circuit for random number generation,” Optica 3, 989–994 (2016).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

C. Abellán, W. Amaya, M. Jofre, M. Curty, A. Acín, J. Capmany, V. Pruneri, and M. W. Mitchell, “Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode,” Opt. Express 22, 1645–1654 (2014).
[Crossref] [PubMed]

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express 19, 20665–20672 (2011).
[Crossref] [PubMed]

Qi, B.

Qian, L.

Raffaelli, F.

Rahn, H.-J.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[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]

Reiserer, A.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Röhlicke, T.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

Ruitenberg, J.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Scheidl, T.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Schneier, B.

C. Hall and B. Schneier, “Remote electronic gambling,” in Proceedings 13th Annual Computer Security Applications Conference, (1997), pp. 232–238.
[Crossref]

Schouten, R. N.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Shalm, L. K.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Shannon, C. E.

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

Shaw, M. D.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Shields, A.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Sibson, P.

Steinlechner, F.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

M. Jofre, M. Curty, F. Steinlechner, G. Anzolin, J. P. Torres, M. W. Mitchell, and V. Pruneri, “True random numbers from amplified quantum vacuum,” Opt. Express 19, 20665–20672 (2011).
[Crossref] [PubMed]

Stern, J. A.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Stevens, M. J.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

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. Photon. 4, 711–715 (2010).
[Crossref]

Syvridis, D.

Tajima, A.

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

Takahashi, S.

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

Taminiau, T. H.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Tanaka, A.

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[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]

Terashima, Y.

Thompson, M. G.

Tomita, A.

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

Torres, J. P.

Tortorici, E.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Twitchen, D. J.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Uchida, A.

Ugajin, K.

Ursin, R.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Verma, V. B.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Vermeulen, R. F.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Versteegh, M. A. M.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Von Neumann, J.

J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Ser. 12, 36–38 (1951).

Wahl, M.

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

Wang, X.

X. Cai and X. Wang, “Stochastic modeling and simulation of gene networks-a review of the state-of-the-art research on stochastic simulations,” IEEE Signal Process. Mag. 24, 27–36 (2007).
[Crossref]

Wayne, M. A.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Wehner, S.

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

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]

Wengerowsky, S.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

Wittmann, B.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[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. Photon. 4, 711–715 (2010).
[Crossref]

Yoshimura, K.

Yuan, Z.

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Zeilinger, A.

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[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]

Zhang, J.

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Zhang, Y.

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

Zimmermanna, H.

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

Appl. Math. Ser. (1)

J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Ser. 12, 36–38 (1951).

Appl. Phys. Lett. (2)

M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, and O. Benson, “An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements,” Appl. Phys. Lett. 98, 171105 (2011).
[Crossref]

Z. Yuan, M. Lucamarini, J. Dynes, B. Fröhlich, A. Plews, and A. Shields, “Robust random number generation using steady-state emission of gain-switched laser diodes,” Appl. Phys. Lett. 104, 261112 (2014).
[Crossref]

Bell Syst. Tech. J. (1)

C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J. 28, 656–715 (1949).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Tajima, A. Tanaka, W. Maeda, S. Takahashi, and A. Tomita, “Practical quantum cryptosystem for metro area applications,” IEEE J. Sel. Top. Quantum Electron. 13, 1031–1038 (2007).
[Crossref]

IEEE Photon. J (1)

A. Khanmohammadi, R. Enne, M. Hofbauer, and H. Zimmermanna, “A monolithic silicon quantum random number generator based on measurement of photon detection time,” IEEE Photon. J 7, 1–13 (2015).
[Crossref]

IEEE Signal Process. Mag. (1)

X. Cai and X. Wang, “Stochastic modeling and simulation of gene networks-a review of the state-of-the-art research on stochastic simulations,” IEEE Signal Process. Mag. 24, 27–36 (2007).
[Crossref]

J. Comput. Chem. (1)

T. H. Click, A. Liu, and G. A. Kaminski, “Quality of random number generators significantly affects results of monte carlo simulations for organic and biological systems,” J. Comput. Chem. 32, 513–524 (2011).
[Crossref]

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]

Nat. Photon. (1)

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. Photon. 4, 711–715 (2010).
[Crossref]

Nat. photonics (1)

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. photonics 4, 511 (2010).
[Crossref]

Nature (1)

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682–686 (2015).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (1)

M. W. Mitchell, C. Abellan, and W. Amaya, “Strong experimental guarantees in ultrafast quantum random number generation,” Phys. Rev. A 91, 012314 (2015).
[Crossref]

Phys. Rev. Lett. (3)

M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-A. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loophole-free test of bell’s theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[Crossref]

L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W. Nam, “Strong loophole-free test of local realism,” Phys. Rev. Lett. 115, 250402 (2015).
[Crossref]

C. Abellán, W. Amaya, D. Mitrani, V. Pruneri, and M. W. Mitchell, “Generation of fresh and pure random numbers for loophole-free bell tests,” Phys. Rev. Lett. 115, 250403 (2015).
[Crossref]

Rev. Sci. Instr. (2)

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]

Y.-Q. Nie, L. Huang, Y. Liu, F. Payne, J. Zhang, and J.-W. Pan, “The generation of 68 gbps quantum random number by measuring laser phase fluctuations,” Rev. Sci. Instr. 86, 063105 (2015).
[Crossref]

Other (1)

C. Hall and B. Schneier, “Remote electronic gambling,” in Proceedings 13th Annual Computer Security Applications Conference, (1997), pp. 232–238.
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Upper: Microscope image of the 4 mm × 7.5 mm Si photonic chip with a one euro cent coin for reference. One such chip can contain up to 20 PD-QESs. A single PD-QES block is less than 0.5 mm × 1 mm. Lower: Schematic of the experimental set-up. The DFB laser is biased using a current source and modulated with a 1 GHz sinusoidal wave. The output pulses with random phases are amplified using an erbium-doped fiber amplifier (EDFA) and coupled into a single mode Si waveguide using an SMF and a GC. The pulses are split in an MMI, with a power splitting ratio of 0.02:0.98, to the two arms of an uMZI, in order to compensate the losses introduced by the longer path. The interference signal is detected using an integrated photodetector and analyzed with a real-time oscilloscope.
Fig. 2
Fig. 2 a) Histogram of the electrically measured interference signal (blue) and noise (green), and simulation of the expected interference signal (black line) and noise (green line). Due to the randomness of the initial phase the accumulated signal follows a bimodal probability distribution. Histograms contain approximately 7 × 105 samples. As confirmed by simulation (black curve), the bimodal distribution corresponds to Eq. 2 with V = 0.763 and random Δϕ. b) Accumulateed interference signal and histogram obtained with the real-time oscilloscope by continously measuring the interfered pulses at a fixed sampling point.
Fig. 3
Fig. 3 Upper: XY plot recorded in the real-time oscilloscope, showing the accumulated occurences of an event (Vn, Vnd) for four different shifts (d = 0, 1, 4, 5). Lower: Simulation of the expected occurences (normalized) for the same values of d. The distribution is expected to be a straight line for d = 0 and a 2D bimodal distribution for d ≠ 0.

Equations (4)

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

t l / t s = exp ( κ Δ l )
P det ( t ) = P l ( t ) + P l ( t + τ ) + 2 V P l ( t ) P l ( t + τ ) cos ( Δ θ + Δ ϕ )
H ( V | N ) = log 2 ( max Pr [ V = v i | N = n i ] ) ,
max Pr [ b = b i | n = n i ] = 2 π arcsin 1 2 + V c 2 Δ V ϕ