Abstract

The low-latency requirements of a practical loophole-free Bell test preclude time-consuming post-processing steps that are often used to improve the statistical quality of a physical random number generator (RNG). Here we demonstrate a post-processing-free RNG that produces a random bit within 2.4(2) ns of an input trigger. We use weak feedback to eliminate long-term drift, resulting in 24 hour operation with output that is statistically indistinguishable from a Bernoulli process. We quantify the impact of the feedback on the predictability of the output as less than 6.4×107 and demonstrate the utility of the Allan variance as a tool for characterizing non-idealities in RNGs.

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

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  1. 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(25), 250402 (2015).
    [Crossref] [PubMed]
  2. P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
    [Crossref] [PubMed]
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2018 (1)

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

2017 (1)

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

2015 (3)

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(25), 250403 (2015).
[Crossref] [PubMed]

M. Stipčević and R. Ursin, “An on-demand optical quantum random number generator with in-future action and ultra-fast response,” Sci. Rep. 5(1), 10214 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

2012 (1)

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref] [PubMed]

2011 (1)

L. Galleani, “The dynamic Allan variance III: confidence and detection surfaces,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(8), 1550–1558 (2011).
[Crossref] [PubMed]

2009 (2)

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

L. Galleani and P. Tavella, “The dynamic Allan variance,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(3), 450–464 (2009).
[Crossref] [PubMed]

1982 (2)

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49(2), 91–94 (1982).
[Crossref]

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49(25), 1804–1807 (1982).
[Crossref]

1981 (1)

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47(7), 460–463 (1981).
[Crossref]

1976 (1)

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37(8), 465–468 (1976).
[Crossref]

1972 (1)

S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28(14), 938–941 (1972).
[Crossref]

1964 (1)

J. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1(3), 195–200 (1964).
[Crossref]

Abellán, 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(25), 250402 (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(25), 250403 (2015).
[Crossref] [PubMed]

Akselrod, G. M.

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

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(25), 250402 (2015).
[Crossref] [PubMed]

Amaya, W.

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(25), 250402 (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(25), 250403 (2015).
[Crossref] [PubMed]

Aspect, A.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49(2), 91–94 (1982).
[Crossref]

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49(25), 1804–1807 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47(7), 460–463 (1981).
[Crossref]

Bell, J.

J. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1(3), 195–200 (1964).
[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(25), 250402 (2015).
[Crossref] [PubMed]

Bierhorst, P.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Chen, G.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

Christensen, B.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Clauser, J. F.

S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28(14), 938–941 (1972).
[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(25), 250402 (2015).
[Crossref] [PubMed]

Curty, M.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref] [PubMed]

Dalibard, J.

A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49(25), 1804–1807 (1982).
[Crossref]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Freedman, S. J.

S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28(14), 938–941 (1972).
[Crossref]

Fry, E.

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37(8), 465–468 (1976).
[Crossref]

Galleani, L.

L. Galleani, “The dynamic Allan variance III: confidence and detection surfaces,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(8), 1550–1558 (2011).
[Crossref] [PubMed]

L. Galleani and P. Tavella, “The dynamic Allan variance,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(3), 450–464 (2009).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Glancy, S.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Grangier, P.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49(2), 91–94 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47(7), 460–463 (1981).
[Crossref]

Guo, L.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Jeffrey, E.

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

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(25), 250402 (2015).
[Crossref] [PubMed]

Jordan, S.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

Knill, E.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[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(25), 250402 (2015).
[Crossref] [PubMed]

Lita, A. 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(25), 250402 (2015).
[Crossref] [PubMed]

Liu, Y.-K.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

Lo, H.-K.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref] [PubMed]

Lu, D.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Mink, A.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Mitchell, M. W.

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(25), 250402 (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(25), 250403 (2015).
[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(25), 250403 (2015).
[Crossref] [PubMed]

Nam, S. W.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Pan, B.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

Pruneri, V.

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(25), 250402 (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(25), 250403 (2015).
[Crossref] [PubMed]

Qi, B.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref] [PubMed]

Roger, G.

A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49(2), 91–94 (1982).
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A. Aspect, J. Dalibard, and G. Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49(25), 1804–1807 (1982).
[Crossref]

A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell’s theorem,” Phys. Rev. Lett. 47(7), 460–463 (1981).
[Crossref]

Rommal, A.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

Shalm, L. K.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[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(25), 250402 (2015).
[Crossref] [PubMed]

Stevens, M. J.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Stipcevic, M.

M. Stipčević and R. Ursin, “An on-demand optical quantum random number generator with in-future action and ultra-fast response,” Sci. Rep. 5(1), 10214 (2015).
[Crossref] [PubMed]

Tavella, P.

L. Galleani and P. Tavella, “The dynamic Allan variance,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(3), 450–464 (2009).
[Crossref] [PubMed]

Thompson, R.

E. Fry and R. Thompson, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 37(8), 465–468 (1976).
[Crossref]

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(25), 250402 (2015).
[Crossref] [PubMed]

Ursin, R.

M. Stipčević and R. Ursin, “An on-demand optical quantum random number generator with in-future action and ultra-fast response,” Sci. Rep. 5(1), 10214 (2015).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Wang, W.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
[Crossref]

Zhang, L.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

Zhang, Y.

P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, and L. K. Shalm, “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature Lett. 556(7700), 223–226 (2018).
[Crossref] [PubMed]

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(25), 250402 (2015).
[Crossref] [PubMed]

Zhao, L.

L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).
[Crossref] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

L. Galleani and P. Tavella, “The dynamic Allan variance,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(3), 450–464 (2009).
[Crossref] [PubMed]

L. Galleani, “The dynamic Allan variance III: confidence and detection surfaces,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(8), 1550–1558 (2011).
[Crossref] [PubMed]

J. Mod. Opt. (1)

M. A. Wayne, E. Jeffrey, G. M. Akselrod, and P. G. Kwiat, “Photon arrival time quantum random number generation,” J. Mod. Opt. 56(4), 516–522 (2009).
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Nature Lett. (1)

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Figures (12)

Fig. 1
Fig. 1 Schematic of the photon-sampling random number generator (PSRNG). A rising edge input to the toggle flip-flop (TFF) initiates the bit-generation process. A 950 ps electrical pulse drives a gain-switched VCSEL, whose output is attenuated and focused onto the active area of a SPAD. Detections are recorded by two flip-flop paths (not-ready and readout), which are clocked at fixed intervals determined by various delays. A logical-1 output from the not-ready DFF2 corresponds to an event for which the SPAD was inactive (not-ready; NR) before the trigger arrived. If the NR output is logical-0 then the output of readout DFF, RND, is the low-latency random bit. Both the RND and NR bits are fed back to the microcontroller (µC) for use in calculating feedback, which is then applied by adjusting the forward bias across the VCSEL with the digital-to-analog converter (DAC).
Fig. 2
Fig. 2 Example photon-arrival-time distribution as measured by a time tagger, and the position of the temporal gating window. Events resulting from detections prior to the start are discarded, and the stop is placed such that timing jitter has a minor effect on the random bit bias.
Fig. 3
Fig. 3 Measured bit-bias resolution of the coarse (left) and fine (right) channels of the DAC. Linear fits are used to estimate the resolutions to be 5.15(6)× 10 7 and 5.32(4)× 10 8 for the coarse and fine channels, respectively. We note that under typical operation, the full range of the fine channel is sufficient to keep the PSRNG balanced to 0.5 (green dashed line).
Fig. 4
Fig. 4 Allan deviation (top) and residuals (bottom) of 96 hours of output with feedback disabled (blue), and an ideal white noise process (red dashed). Significant deviation occurs for sampling intervals greater than 10 3 . Although not illustrated, no significant deviation was revealed for sampling intervals < 1 s, suggesting the absence of shorter-term non-white noise.
Fig. 5
Fig. 5 Collection of 44 dynamic Allan deviation calculations and σ = 0.99 confidence surfaces (heavy red line) expected for an ideal white noise source. The tight grouping of the individual plots indicates that without feedback the PSRNG is statistically indistinguishable from a white noise process over these sampling intervals. The DADEV is typically illustrated as a 3D surface, however, since no instabilities were visible we displayed the 2D plot.
Fig. 6
Fig. 6 The filtering and feedback scheme. By designing an appropriate digital filter f(t), the random walk can be subtracted off, leaving a random signal well approximated by white noise.
Fig. 7
Fig. 7 The DFT of the feedback-disabled (red) PSRNG’s bit bias p demonstrates that the uncontrolled system deviates from white noise for frequencies below 2× 10 4 Hz. No discernable deviations occurred at higher frequencies. After feedback (blue), these frequency components are significantly reduced.
Fig. 8
Fig. 8 Sum of the magnitudes of the residual between the Allan deviations of ideal white noise and the filtered data for various gains with a window length M = 512. The minimum occurs at a gain of approximately 0.32 / M 2 .
Fig. 9
Fig. 9 Histogram of the differences between successive fine DAC register values for a 96 hour data set. The majority of the time the feedback value is actually 0 bits (no change), while the largest change is ± 6 DAC bits, or Δp=3.19× 10 7 .
Fig. 10
Fig. 10 Allan deviation (top), and its residual difference from white noise (bottom), out to τ=1× 10 5 for the measured PSRNG’s output with (red) and without (green) feedback, along with simulated results generated by applying the feedback in software to a free-running data set (blue). For comparison, the Allan deviation of white noise is also shown (black).
Fig. 11
Fig. 11 Bit bias for the PSRNG with (blue) and without (red) feedback enabled, when averaged into 1000 sample blocks. The random walk noise has been reduced, resulting in a stationary process centered around the desired mean.
Fig. 12
Fig. 12 Proportion of passing values for the frequency (monobit) test without (red) and with (blue) feedback [13]. A minimum of 96 passes out of 100 (solid magenta line) are needed to conclude the sequence is behaving randomly. With feedback enabled the output of the PSRNG appears random until ≈2300 blocks of 100 seconds each have been sampled, or 64 hours. After this period there are enough statistics for the test suite to identify the influence of the weak feedback used to eliminate drift.

Equations (4)

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σ y 2 ( τ )= 1 2(M1) i=1 M1 [ y i+1 y i ] 2 ,
e( t )=g m=0 M1 [ n 1 ( tm )(50 000) ].
y n =( 1g ) y n1 g y n2 g y 0 +( x n x n1 ),
z m ( 1g ) z m1 +g i=0 m2 z i =0.

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