Abstract

The manipulation of high-dimensional degrees of freedom provides new opportunities for more efficient quantum information processing. It has recently been shown that high-dimensional encoded states can provide significant advantages over binary quantum states in applications of quantum computation and quantum communication. In particular, high-dimensional quantum key distribution enables higher secret-key generation rates under practical limitations of detectors or light sources, as well as greater error tolerance. Here, we demonstrate high-dimensional quantum key distribution capabilities both in the laboratory and over a deployed fiber, using photons encoded in a high-dimensional alphabet to increase the secure information yield per detected photon. By adjusting the alphabet size, it is possible to mitigate the effects of receiver bottlenecks and optimize the secret-key rates for different channel losses. This work presents a strategy for achieving higher secret-key rates in receiver-limited scenarios and marks an important step toward high-dimensional quantum communication in deployed fiber networks.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (6)

S. Muralidharan, C.-L. Zou, L. Li, J. Wen, and L. Jiang, “Overcoming erasure errors with multilevel systems,” New J. Phys. 19, 013026 (2017).
[Crossref]

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Information 3, 25 (2017).
[Crossref]

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Science Advances 3, e1701491 (2017).
[Crossref] [PubMed]

B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4, 1006–1010 (2017).
[Crossref]

2016 (2)

M. Y. Niu, F. Xu, J. H. Shapiro, and F. Furrer, “Finite-key analysis for time-energy high-dimensional quantum key distribution,” Phys. Rev. A 94, 052323 (2016).
[Crossref]

H. Bao, W. Bao, Y. Wang, C. Zhou, and R. Chen, “Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution,” J. Phys. A: Mathematical and Theoretical 49, 205301 (2016).
[Crossref]

2015 (6)

D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
[Crossref]

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photon. 9, 163–168 (2015).
[Crossref]

C. Lee, J. Mower, Z. Zhang, J. Shapiro, and D. Englund, “Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution,” Quantum Inf. Process. 14, 1005–1015 (2015).
[Crossref]

M. Lucamarini, I. Choi, M. B. Ward, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical security bounds against the trojan-horse attack in quantum key distribution,” Phys. Rev. X 5, 031030 (2015).

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
[Crossref]

2014 (5)

C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
[Crossref]

L. C. Comandar, B. Fröhlich, M. Lucamarini, K. A. Patel, A. W. Sharpe, J. F. Dynes, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Room temperature single-photon detectors for high bit rate quantum key distribution,” Appl. Phys. Lett. 104, 021101 (2014).
[Crossref]

E. A. Dauler, M. E. Grein, A. J. Kerman, F. Marsili, S. Miki, S. W. Nam, M. D. Shaw, H. Terai, V. B. Verma, and T. Yamashita, “Review of superconducting nanowire single-photon detector system design options and demonstrated performance,” Opt. Eng. 53, 081907 (2014).
[Crossref]

Z. Zhang, J. Mower, D. Englund, F. N. C. Wong, and J. H. Shapiro, “Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry,” Phys. Rev. Lett. 112, 120506 (2014).
[Crossref] [PubMed]

R. Valivarthi, I. Lucio-Martinez, A. Rubenok, P. Chan, F. Marsili, V. B. Verma, M. D. Shaw, J. A. Stern, J. A. Slater, D. Oblak, S. W. Nam, and W. Tittel, “Efficient Bell state analyzer for time-bin qubits with fast-recovery WSi superconducting single photon detectors,” Opt. Express 22, 24497–24506 (2014).
[Crossref] [PubMed]

2013 (7)

D. Rosenberg, A. J. Kerman, R. J. Molnar, and E. A. Dauler, “High-speed and high-efficiency superconducting nanowire single photon detector array,” Opt. Express 21, 1440–1447 (2013).
[Crossref] [PubMed]

J. Nunn, L. J. Wright, C. Söller, L. Zhang, I. A. Walmsley, and B. J. Smith, “Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion,” Opt. Express 21, 15959–15973 (2013).
[Crossref] [PubMed]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

A. J. Kerman, D. Rosenberg, R. J. Molnar, and E. A. Dauler, “Readout of superconducting nanowire single-photon detectors at high count rates,” J. Appl. Phys. 113, 144511 (2013).
[Crossref]

J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
[Crossref]

S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref] [PubMed]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon. 7, 210–214 (2013).
[Crossref]

2012 (1)

2011 (1)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

2010 (1)

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81, 062343 (2010).
[Crossref]

2009 (2)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

D. Stucki, N. Walenta, F. Vannel, R. T. Thew, N. Gisin, H. Zbinden, S. Gray, C. R. Towery, and S. Ten, “High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres,” New J. Phys. 11, 075003 (2009).
[Crossref]

2007 (3)

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 54, 337–352 (2007).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13, 978–983 (2007).
[Crossref]

2006 (3)

B. S. Robinson, A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. Yang, and K. K. Berggren, “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett. 31, 444–446 (2006).
[Crossref] [PubMed]

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88, 111116 (2006).
[Crossref]

S. Gröblacher, T. Jennewein, A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[Crossref]

2005 (3)

H.-K. Lo, H. F. Chau, and M. Ardehali, “Efficient quantum key distribution scheme and a proof of its unconditional security,” J. Cryptology 18, 133–165 (2005).
[Crossref]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
[Crossref] [PubMed]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

2002 (1)

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

2000 (2)

H. Bechmann-Pasquinucci and W. Tittel, “Quantum cryptography using larger alphabets,” Phys. Rev. A 61, 062308 (2000).
[Crossref]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Ali-Khan, I.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large-alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. Lett. 98, 060503 (2007).
[Crossref] [PubMed]

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[Crossref]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

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B. S. Robinson, A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. Yang, and K. K. Berggren, “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett. 31, 444–446 (2006).
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W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
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A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
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N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Science Advances 3, e1701491 (2017).
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S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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Cardenas, J.

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Choi, I.

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Comandar, L. C.

B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
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L. C. Comandar, B. Fröhlich, M. Lucamarini, K. A. Patel, A. W. Sharpe, J. F. Dynes, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Room temperature single-photon detectors for high bit rate quantum key distribution,” Appl. Phys. Lett. 104, 021101 (2014).
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G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Information 3, 25 (2017).
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E. A. Dauler, M. E. Grein, A. J. Kerman, F. Marsili, S. Miki, S. W. Nam, M. D. Shaw, H. Terai, V. B. Verma, and T. Yamashita, “Review of superconducting nanowire single-photon detector system design options and demonstrated performance,” Opt. Eng. 53, 081907 (2014).
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A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88, 111116 (2006).
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S. A. Castelletto, I. P. Degiovanni, V. Schettini, and A. L. Migdall, “Reduced deadtime and higher rate photon-counting detection using a multiplexed detector array,” J. Mod. Opt. 54, 337–352 (2007).
[Crossref]

V. Schettini, S. V. Polyakov, I. P. Degiovanni, G. Brida, S. Castelletto, and A. L. Migdall, “Implementing a multiplexed system of detectors for higher photon counting rates,” IEEE J. Sel. Top. Quantum Electron. 13, 978–983 (2007).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
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M. Lucamarini, I. Choi, M. B. Ward, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical security bounds against the trojan-horse attack in quantum key distribution,” Phys. Rev. X 5, 031030 (2015).

L. C. Comandar, B. Fröhlich, M. Lucamarini, K. A. Patel, A. W. Sharpe, J. F. Dynes, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Room temperature single-photon detectors for high bit rate quantum key distribution,” Appl. Phys. Lett. 104, 021101 (2014).
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Elser, D.

Englund, D.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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C. Lee, J. Mower, Z. Zhang, J. Shapiro, and D. Englund, “Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution,” Quantum Inf. Process. 14, 1005–1015 (2015).
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Z. Zhang, J. Mower, D. Englund, F. N. C. Wong, and J. H. Shapiro, “Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry,” Phys. Rev. Lett. 112, 120506 (2014).
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C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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Englund, D. R.

D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
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S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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Fickler, R.

Figueroa, M.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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Forbes, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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Fröhlich, B.

B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
[Crossref]

L. C. Comandar, B. Fröhlich, M. Lucamarini, K. A. Patel, A. W. Sharpe, J. F. Dynes, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Room temperature single-photon detectors for high bit rate quantum key distribution,” Appl. Phys. Lett. 104, 021101 (2014).
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M. Y. Niu, F. Xu, J. H. Shapiro, and F. Furrer, “Finite-key analysis for time-energy high-dimensional quantum key distribution,” Phys. Rev. A 94, 052323 (2016).
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Gauthier, D. J.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Science Advances 3, e1701491 (2017).
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M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
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Gerrits, T.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photon. 7, 210–214 (2013).
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Gilchrist, A.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
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Giovannini, D.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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Gisin, N.

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photon. 9, 163–168 (2015).
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D. Stucki, N. Walenta, F. Vannel, R. T. Thew, N. Gisin, H. Zbinden, S. Gray, C. R. Towery, and S. Ten, “High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres,” New J. Phys. 11, 075003 (2009).
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N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000).
[Crossref] [PubMed]

Gol’tsman, G.

A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88, 111116 (2006).
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Gómez, E.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
[Crossref]

Gómez, E. S.

S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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González, P.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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Goyal, S.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81, 062343 (2010).
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D. Stucki, N. Walenta, F. Vannel, R. T. Thew, N. Gisin, H. Zbinden, S. Gray, C. R. Towery, and S. Ten, “High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres,” New J. Phys. 11, 075003 (2009).
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Grein, M. E.

E. A. Dauler, M. E. Grein, A. J. Kerman, F. Marsili, S. Miki, S. W. Nam, M. D. Shaw, H. Terai, V. B. Verma, and T. Yamashita, “Review of superconducting nanowire single-photon detector system design options and demonstrated performance,” Opt. Eng. 53, 081907 (2014).
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Günthner, K.

Guo, G.-C.

Guo, J.-F.

Hamilton, S. A.

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S. Muralidharan, C.-L. Zou, L. Li, J. Wen, and L. Jiang, “Overcoming erasure errors with multilevel systems,” New J. Phys. 19, 013026 (2017).
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B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photon. 9, 163–168 (2015).
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B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
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M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
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C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
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Wright, L. J.

Xavier, G. B.

G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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M. Y. Niu, F. Xu, J. H. Shapiro, and F. Furrer, “Finite-key analysis for time-energy high-dimensional quantum key distribution,” Phys. Rev. A 94, 052323 (2016).
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E. A. Dauler, M. E. Grein, A. J. Kerman, F. Marsili, S. Miki, S. W. Nam, M. D. Shaw, H. Terai, V. B. Verma, and T. Yamashita, “Review of superconducting nanowire single-photon detector system design options and demonstrated performance,” Opt. Eng. 53, 081907 (2014).
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Yuan, Z.

Yuan, Z. L.

M. Lucamarini, I. Choi, M. B. Ward, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical security bounds against the trojan-horse attack in quantum key distribution,” Phys. Rev. X 5, 031030 (2015).

L. C. Comandar, B. Fröhlich, M. Lucamarini, K. A. Patel, A. W. Sharpe, J. F. Dynes, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Room temperature single-photon detectors for high bit rate quantum key distribution,” Appl. Phys. Lett. 104, 021101 (2014).
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Zhang, L.

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C. Lee, J. Mower, Z. Zhang, J. Shapiro, and D. Englund, “Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution,” Quantum Inf. Process. 14, 1005–1015 (2015).
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D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
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Z. Zhang, J. Mower, D. Englund, F. N. C. Wong, and J. H. Shapiro, “Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry,” Phys. Rev. Lett. 112, 120506 (2014).
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J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A 87, 062322 (2013).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
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C. Lee, Z. Zhang, G. R. Steinbrecher, H. Zhou, J. Mower, T. Zhong, L. Wang, X. Hu, R. D. Horansky, V. B. Verma, A. E. Lita, R. P. Mirin, F. Marsili, M. D. Shaw, S. W. Nam, G. W. Wornell, F. N. C. Wong, J. H. Shapiro, and D. Englund, “Entanglement-based quantum communication secured by nonlocal dispersion cancellation,” Phys. Rev. A 90, 062331 (2014).
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H. Zhou, L. Wang, and G. Wornell, “Layered schemes for large-alphabet secret key distribution,” in Proceediings of Information Theory and Applications Workshop (ITA) (IEEE, 2013), pp. 1–10.

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Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Information 3, 25 (2017).
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A. J. Kerman, E. A. Dauler, W. E. Keicher, J. K. W. Yang, K. K. Berggren, G. Gol’tsman, and B. Voronov, “Kinetic-inductance-limited reset time of superconducting nanowire photon counters,” Appl. Phys. Lett. 88, 111116 (2006).
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H. Bao, W. Bao, Y. Wang, C. Zhou, and R. Chen, “Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution,” J. Phys. A: Mathematical and Theoretical 49, 205301 (2016).
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S. Muralidharan, C.-L. Zou, L. Li, J. Wen, and L. Jiang, “Overcoming erasure errors with multilevel systems,” New J. Phys. 19, 013026 (2017).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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npj Quantum Information (1)

Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, “High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,” npj Quantum Information 3, 25 (2017).
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Opt. Eng. (1)

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Optica (2)

Phys. Rev. A (8)

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M. Y. Niu, F. Xu, J. H. Shapiro, and F. Furrer, “Finite-key analysis for time-energy high-dimensional quantum key distribution,” Phys. Rev. A 94, 052323 (2016).
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G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. Connolly, A. Przysiezna, E. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A 96, 022317 (2017).
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D. Bunandar, Z. Zhang, J. H. Shapiro, and D. R. Englund, “Practical high-dimensional quantum key distribution with decoy states,” Phys. Rev. A 91, 022336 (2015).
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Z. Zhang, J. Mower, D. Englund, F. N. C. Wong, and J. H. Shapiro, “Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry,” Phys. Rev. Lett. 112, 120506 (2014).
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Phys. Rev. X (1)

M. Lucamarini, I. Choi, M. B. Ward, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Practical security bounds against the trojan-horse attack in quantum key distribution,” Phys. Rev. X 5, 031030 (2015).

Quantum Inf. Process. (1)

C. Lee, J. Mower, Z. Zhang, J. Shapiro, and D. Englund, “Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution,” Quantum Inf. Process. 14, 1005–1015 (2015).
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Sci. Rep. (1)

S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Science Advances 3, e1701491 (2017).
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C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, 1984), pp. 175–179.

H. Zhou, L. Wang, and G. Wornell, “Layered schemes for large-alphabet secret key distribution,” in Proceediings of Information Theory and Applications Workshop (ITA) (IEEE, 2013), pp. 1–10.

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Figures (3)

Fig. 1
Fig. 1 (a) In high-dimensional temporal encoding (pulse position modulation), information is encoded in the position of an optical pulse within M slots, depicted here for alphabet size M ∈ {2, 4, 8, 16}. For a fixed slot duration, the alphabet size and the transmitted pulse rate are inversely proportional. (b) Representative plot of secret-key rate versus channel length for a traditional two-dimensional QKD protocol, assuming a 5 Gbps modulation rate, a 0.2 dB/km channel loss, a 1 kcps background count rate, a 93% detector efficiency, and a 100 ns detector reset time after each detection event. These detector performance characteristics were chosen to correspond with the high efficiency telecom band single photon detection system reported in [22], and the effects of detector reset time on observed count rate were modeled following [37]. Three regions are denoted: I. At short distances, 0–90 km (or correspondingly, low losses, 0–18 dB), the secret-key rate is limited by detector saturation. II. For higher losses (normal operation), the secret-key rate decays exponentially with distance. III. At even higher losses (> 300 km), a cutoff is reached when Bob’s received photon rate becomes comparable to his detectors’ background count rate. At this point, the error rate grows and the secret-key rate drops abruptly.
Fig. 2
Fig. 2 Map showing node locations and approximate path of the installed 43-km deployed-fiber testbed used in this work. Overlaid are Alice’s transmitter, located in Cambridge, MA, and Bob’s receiver, located in Lexington, MA. BPF: bandpass filter. EOM: electro-optic modulator. VOA: variable attenuator. ND: normal GVD. AD: anomalous GVD. DCF: dispersion-compensating fiber.
Fig. 3
Fig. 3 (a) Experimental (stars) and theoretical (dashed curves) secret-key rates versus channel loss. Colors correspond to optimal alphabet size M for each of the channel configurations. Each theoretical curve is based on the experimental parameters (e.g., detector timing jitter) observed in the corresponding the channel configuration. The theoretical secret-key rate for M = 2 over the deployed fiber channel is also plotted for reference. (b) Experimental secret-key rates for all alphabet sizes of each channel configuration. Loss increases from left to right. The optimal M increases as loss decreases. For experimental convenience, we did not increase the alphabet size once it became apparent that doing so would not increase the secret-key rate.

Tables (2)

Tables Icon

Table 1 Summary of the maximum secret-key rates obtained in the three channel configurations.

Tables Icon

Table 2 Numerical values of security-related parameters for the three channel configurations.

Equations (1)

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r , decoy = β I ( A ; B ) ( 1 F μ LB ) log 2 M F μ LB χ UB ( A ; E ) ,

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