Secure quantum key distribution

Journal name:
Nature Photonics
Year published:
Published online


Secure communication is crucial in the Internet Age, and quantum mechanics stands poised to revolutionize cryptography as we know it today. In this Review, we introduce the motivation and the current state of the art of research in quantum cryptography. In particular, we discuss the present security model together with its assumptions, strengths and weaknesses. After briefly introducing recent experimental progress and challenges, we survey the latest developments in quantum hacking and countermeasures against it.

At a glance


  1. Progress in free-space QKD implementations.
    Figure 1: Progress in free-space QKD implementations.

    a, First free-space demonstration of QKD19 realized two decades ago over a distance of 32 cm. The system uses a light-emitting diode (LED) in combination with Pockels cells to prepare and measure the different signal states. b, Entanglement-based QKD set-up connecting the two Canary Islands La Palma and Tenerife6. The optical link is 144 km long. OGS, optical ground station; GPS, Global Positioning System; PBS, polarizing beamsplitter; BS, beamsplitter; HWP, half-wave plate. c, Schematic of a decoy-state BB84 QKD experiment between ground and a hot-air balloon20. This demonstration may be considered a first step towards realizing QKD between ground and low-Earth-orbit satellites. MON, monitor window; ATT, attenuator; DM, dichroic mirror; 532LD, 532 nm laser; FSM, fast steering mirror; 671LD, 671 nm laser; 532D, 532 nm detector; IF, interference filter; CMOS, complementary metal–oxide–semiconductor. Figure adapted with permission from: a, ref. 19, © 1992 IACR; b, ref. 6, © 2007 NPG; c, ref. 20, © 2013 NPG.

  2. Experimental QKD.
    Figure 2: Experimental QKD.

    a, Schematic of the decoy-state BB84 protocol26, 27, 28, 29, 30, 31, 32, 33, 34, 35 based on polarization coding. Four lasers are used to prepare the polarizations needed in BB84. Decoy states are generated with an amplitude modulator (AM). On Bob's side, a 50:50 beamsplitter (BS) is used to passively ensure a random measurement basis choice. Active receivers are also common. PM, phase modulator; F, optical filter; I, optical isolator; HWP, half-wave plate; PBS, polarizing beamsplitter; QRNG, quantum random number generator. b, Lower bound on the secret key rate (per pulse) in logarithmic scale for a BB84 set-up with two decoys (blue line)29. In the short-distance regime, the key rate scales linearly with the transmittance, η. Standard BB84 protocol without decoy states (dark brown line)23, 25; its key rate scales as η2. c, Photograph of a fibre-coupled modularly integrated decoy-state BB84 transmitter based on polarization coding37; it produces decoy-state BB84 signals at a repetition rate of 10 MHz. d, Performance of the SwissQuantum network9. This network was operated for more than 18 months in Geneva, Switzerland. The data shown in the figure correspond to a QKD link of 14.4 km; they highlight the stability of current QKD set-ups. QBER, quantum bit error rate. Figure adapted with permission from: c, ref. 37, © 2013 LANL; d, ref. 9, © 2011 IOP.

  3. QKD networks.
    Figure 3: QKD networks.

    a, Schematic of the layer structure of the Tokyo QKD network13, which is based on a trusted node architecture. From the users' perspective, the QKD layer and the key management layer can be treated as a black box that supplies them with a secure key. They can be used in applications such as secure video meetings and secure communication via smart phones. Different QKD networks have been implemented in other countries (see, for instance, refs 7,8,9,10,11,12). b, (Upper subfigure) Downstream versus upstream passive quantum access network. In the upstream approach14, single-photon detectors are located only at the network node. This may reduce the costs of the network and allow its detectors' bandwidth to be used more efficiently. Estimated secret key rate per user for an upstream solution as a function of the distance and the number of active users in the network for various network capacities (lower subfigure). Figure b adapted with permission from ref. 14 © 2013 NPG.

  4. Examples of quantum hacking.
    Figure 4: Examples of quantum hacking.

    a, Experimentally measured detection efficiency mismatch between two detectors from a commercial QKD system versus time shifts76. Eve could exploit this to perform a time-shift attack75; that is, she could shift the arrival time of each signal such that one detector has a much higher detection efficiency than the other. b, Working principle of the detector blinding attack80. By shining intense light onto the detectors, Eve can make them leave Geiger-mode operation (used in QKD) and enter linear-mode operation. In so doing, she can control which detector produces a 'click' each given time and learn the entire secret key without being detected. c, Full-field implementation of a detector blinding attack on a running entanglement-based QKD set-up83. HWP, half-wave plate; PBS, polarizing beamsplitter; BS, beamsplitter; LD, laser diode; SPDC, spontaneous parametric downconversion, BBO; β-barium-borate crystal; FPC, fibre polarization controller; TS, timestamp unit; PA, polarization analyser; FSG, faked-state generator. Figure adapted with permission from: a, ref. 76 © 2008 APS; b, ref. 80 © 2010 NPG; c, ref. 83 © 2011 NPG.

  5. Examples of countermeasures against quantum hacking.
    Figure 5: Examples of countermeasures against quantum hacking.

    a, Schematic of DI-QKD96, 97, 98, 9. Alice and Bob can prove the security of the protocol based on the violation of an appropriate Bell inequality. To overcome the channel loss, the system can include a fair-sampling device100, 101. In principle, DI-QKD can remove all side channels in a QKD implementation. b, Schematic representation of MDI-QKD74. Alice and Bob prepare WCPs in different BB84 polarization states and send them to an untrusted relay Charles, who is supposed to perform a Bell-state measurement that projects the incoming signals into a Bell state. MDI-QKD removes all detector side channels, which can be regarded as the Achilles heel of QKD. MDI-QKD has the advantage over DI-QKD of being feasible with current technology. Indeed, proof-of-principle demonstrations have been already done104, 105, and real QKD implementations have been realized106, 107. BS, beamsplitter; PBS, polarizing beamsplitter; D, single-photon detector. c, Field-test proof-of-principle demonstration of MDI-QKD realized in Calgary, Canada104. MC, master clock; AM, amplitude modulator; PM, phase modulator; ATT, variable attenuator; POC, polarization controller; FS, frequency shifter. Figure c reproduced with permission from ref. 104 © 2013 APS.


  1. Rivest, R. L., Shamir, A. & Adleman, L. M. A method of obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120126 (1978).
  2. Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. in Proc. 35th Ann. Symp. Found. Comp. Sci. (ed. Goldwasser, S.) 124134 (IEEE, 1994).
  3. Ben-Or, M., Horodecki, M., Leung, D. W., Mayers, D. & Oppenheim, J. The universal composable security of quantum key distribution. in Theory of Cryptography (ed. Kilian, J.) 3378, 386406 (Springer, 2005).
  4. Renner, R. & König, R. Universally composable privacy amplification against quantum adversaries. in Theory of Cryptography (ed. Kilian, J.) 3378, 407425 (Springer, 2005).
  5. Yoshino, K., Ochi, T., Fujiwara, M., Sasaki, M. & Tajima, A. Maintenance-free operation of WDM quantum key distribution system through a field fiber over 30 days. Opt. Express 21, 3139531401 (2013).
  6. Ursin, R. et al. Entanglement-based quantum communication over 144 km. Nature Phys. 3, 481486 (2007).
  7. Elliott, C. et al. Current status of the DARPA Quantum Network. in Proc. SPIE (eds Donkor, E. J., Pirich, A. R. & Brandt, H. E.) 5815, 138149 (SPIE, 2005).
  8. Peev, M. et al. The SECOQC quantum key distribution network in Vienna. New J. Phys. 11, 075001 (2009).
  9. Stucki, D. et al. Long-term performance of the SwissQuantum quantum key distribution network in a field environment. New J. Phys. 13, 123001 (2011).
  10. Chen, T.-Y. et al. Field test of a practical secure communication network with decoy-state quantum cryptography. Opt. Express 17, 65406549 (2009).
  11. Chen, T.-Y. et al. Metropolitan all-pass and inter-city quantum communication network. Opt. Express 18, 2721727225 (2010).
  12. Wang, S. et al. Field test of wavelength-saving quantum key distribution network. Opt. Lett. 35, 24542456 (2010).
  13. Sasaki, M. et al. Field test of quantum key distribution in the Tokyo QKD network. Opt. Express 19, 1038710409 (2011).
  14. Fröhlich, B. et al. A quantum access network. Nature 501, 6972 (2013).
  15. Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nature Photon. 7, 210214 (2013).
  16. Rosenberg, D., Kerman, A. J., Molnar, R. J. & Dauler, E. A. High-speed and high-efficiency superconducting nanowire single photon detector array. Opt. Express 21, 14401447 (2013).
  17. Miki, S., Yamashita, T., Terai, H. & Wang, Z. High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler. Opt. Express 21, 1020810214 (2013).
  18. Restelli, A., Bienfang, J. C. & Migdall, A. L. Single-photon detection efficiency up to 50% at 1310 nm with an InGaAs/InP avalanche diode gated at 1.25 GHz. Appl. Phys. Lett. 102, 141104 (2013).
  19. Bennett, C. H., Bessette, F., Brassard, G., Salvail, L. & Smolin, J. Experimental quantum cryptography. J. Cryptol. 5, 328 (1992).
  20. Wang, J.-Y. et al. Direct and full-scale experimental verifications towards ground-satellite quantum key distribution. Nature Photon. 7, 387393 (2013).
  21. Nauerth, S. et al. Air-to-ground quantum communication. Nature Photon. 7, 382386 (2013).
  22. Lim, C. C. W., Curty, M., Walenta, N., Xu, F. & Zbinden, H. Concise security bounds for practical decoy-state quantum key distribution. Phys. Rev. A 89, 022307 (2014).
  23. Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. in Proc. IEEE Int. Conf. Comp. Systems Signal Processing 175179 (IEEE, 1984).
  24. Huttner, B., Imoto, N., Gisin, N. & Mor, T. Quantum cryptography with coherent states. Phys. Rev. A 51, 18631869 (1995).
  25. Gottesman, D., Lo, H.-K., Lütkenhaus, N. & Preskill, J. Security of quantum key distribution with imperfect devices. Quant. Inf. Comp. 5, 325360 (2004).
  26. Hwang, W.-Y. Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003).
  27. Lo, H.-K., Ma, X. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).
  28. Wang, X.-B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).
  29. Ma, X., Qi, B., Zhao, Y. & Lo, H.-K. Practical decoy state for quantum key distribution. Phys. Rev. A 72, 012326 (2005).
  30. Zhao, Y., Qi, B., Ma, X., Lo, H.-K. & Qian, L. Experimental quantum key distribution with decoy states. Phys. Rev. Lett. 96, 070502 (2006).
  31. Peng, C.-Z. et al. Experimental long-distance decoy-state quantum key distribution based on polarization encoding. Phys. Rev. Lett. 98, 010505 (2007).
  32. Rosenberg, D. et al. Long-distance decoy-state quantum key distribution in optical fiber. Phys. Rev. Lett. 98, 010503 (2007).
  33. Schmitt-Manderbach, T. et al. Experimental demonstration of free-space decoy-state quantum key distribution over 144 km. Phys. Rev. Lett. 98, 010504 (2007).
  34. Yuan, Z. L., Sharpe, A. W. & Shields, A. J. Unconditionally secure one-way quantum key distribution using decoy pulses. Appl. Phys. Lett. 90, 011118 (2007).
  35. Liu, Y. et al. Decoy-state quantum key distribution with polarized photons over 200 km. Opt. Express 18, 85878594 (2010).
  36. Wehner, S., Curty, M., Schaffner, C. & Lo, H.-K. Implementation of two-party protocols in the noisy-storage model. Phys. Rev. A 81, 052336 (2010).
  37. Hughes, R. J. et al. Network-centric quantum communications with application to critical infrastructure protection. Preprint at (2013).
  38. Ekert, A. K. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett. 67, 661663 (1991).
  39. Ma, X., Fung, C.-H. F. & Lo, H.-K. Quantum key distribution with entangled photon sources. Phys. Rev. A 76, 012307 (2007).
  40. Treiber, A. et al. Fully automated entanglement-based quantum cryptography system for telecom fiber networks. New J. Phys. 11, 045013 (2009).
  41. Poppe, A. et al. Practical quantum key distribution with polarization-entangled photons. Opt. Express 12, 38653871 (2004).
  42. Inoue, K., Waks, E. & Yamamoto, Y. Differential phase shift quantum key distribution. Phys. Rev. Lett. 89, 037902 (2002).
  43. Takesue, H. et al. Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors. Nature Photon. 1, 343348 (2007).
  44. Stucki, D. et al. High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres. New J. Phys. 11, 075003 (2009).
  45. Grosshans, F. et al. Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238241 (2003).
  46. Qi, B., Huang, L.-L., Qian, L. & Lo, H.-K. Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers. Phys. Rev. A 76, 052323 (2007).
  47. Jouguet, P., Kunz-Jacques, S., Leverrier, A., Grangier, P. & Diamanti, E. Experimental demonstration of long-distance continuous-variable quantum key distribution. Nature Photon. 7, 378381 (2013).
  48. Yuan, Z. L., Kardynal, B. E., Sharpe, A. W. & Shields, A. J. High speed single photon detection in the near infrared. App. Phys. Lett. 91, 041114 (2007).
  49. Dixon, A. R. et al. Ultrashort dead time of photon-counting InGaAs avalanche photodiodes. Appl. Phys. Lett. 94, 231113 (2009).
  50. Namekata, N., Sasamori, S. & Inoue, S. 800 MHz single-photon detection at 1550-nm using an InGaAs/InP avalanche photodiode operated with a sine wave gating. Opt. Express 14, 1004310049 (2006).
  51. Liang, X.-L. et al. Fully integrated InGaAs/InP single-photon detector module with gigahertz sine wave gating. Rev. Sci. Instrum. 83, 083111 (2012).
  52. Wu, Q.-L., Namekata, N. & Inoue, S. Sinusoidally gated InGaAs avalanche photodiode with direct hold-off function for efficient and low-noise single-photon detection. Appl. Phys. Express 6, 062202 (2013).
  53. Zhang, J., Thew, R., Barreiro, C. & Zbinden, H. Practical fast gate rate InGaAs/InP single-photon avalanche photodiodes. Appl. Phys. Lett. 95, 091103 (2009).
  54. Shibata, H., Takesue, H., Honjo, T., Akazaki, T. & Tokura, Y. Single-photon detection using magnesium diboride superconducting nanowires. Appl. Phys. Lett. 97, 212504 (2010).
  55. Pironio, S. et al. Random numbers certified by Bell's theorem. Nature 464, 10211024 (2010).
  56. Williams, C. R. S., Salevan, J. C., Li, X., Roy, R. & Murphy, T. E. Fast physical random number generator using amplified spontaneous emission. Opt. Express 18, 2358423597 (2010).
  57. Jofre, M. et al. True random numbers from amplified quantum vacuum. Opt. Express 19, 2066520672 (2011).
  58. Abellán, C. et al. Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode. Opt. Express 22, 16451654 (2014).
  59. Qi, B., Chi, Y.-M., Lo, H.-K. & Qian, L. High-speed quantum random number generation by measuring phase noise of a single-mode laser. Opt. Lett. 35, 312314 (2010).
  60. Dixon, A. R., Yuan, Z. L., Dynes, J. F., Sharpe, A. W. & Shields, A. J. Continuous operation of high bit rate quantum key distribution. Appl. Phys. Lett. 96, 161102 (2010).
  61. Choi, I., Young, R. J. & Townsend, P. D. Quantum key distribution on a 10Gb/s WDM-PON. Opt. Express 18, 96009612 (2010).
  62. Patel, K. A. et al. Coexistence of high-bit-rate quantum key distribution and data on optical fiber. Phys. Rev. X 2, 041010 (2012).
  63. Chapuran, T. E. et al. Optical networking for quantum key distribution and quantum communications. New J. Phys. 11, 105001 (2009).
  64. Patel, K. A. et al. Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks. Appl. Phys. Lett. 104, 051123 (2014).
  65. Dixon, A. R., Yuan, Z. L., Dynes, J. F., Sharpe, A. W. & Shields, A. J. Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate. Opt. Express 16, 1879018979 (2008).
  66. Zhang, Q. et al. Megabits secure key rate quantum key distribution. New J. Phys. 11, 045010 (2009).
  67. Tanaka, A. et al. High-speed quantum key distribution system for 1-Mbps real-time key generation. IEEE J. Quant. Electron. 48, 542550 (2012).
  68. Walenta, N. et al. 1 Mbps coherent one-way QKD with dense wavelength division multiplexing and hardware key distillation. in Proc. 2nd Ann. Conf. Quantum Cryptography (2012).
  69. Qi, B., Zhu, W., Qian, L. & Lo, H.-K. Feasibility of quantum key distribution through dense wavelength division multiplexing network. New J. Phys. 12, 103042 (2010).
  70. Jouguet, P. et al. Experimental demonstration of the coexistence of continuous-variable quantum key distribution with an intense DWDM classical channel. in Proc. 3rd Ann. Conf. Quantum Cryptography (2013).
  71. Raymer, M. G., Cooper, J., Carmichael, H. J., Beck M. & Smithey, D. T. Ultrafast measurement of optical-field statistics by dc-balanced homodyne detection. J. Opt. Soc. Am. B 12, 18011812 (1995).
  72. Hayashi, M. & Tsurumaru, T. Concise and tight security analysis of the Bennett–Brassard 1984 protocol with finite key lengths. New J. Phys. 14, 093014 (2012).
  73. Curty, M. et al. Finite-key analysis for measurement-device-independent quantum key distribution. Nature Commun. 5, 3732 (2014).
  74. Lo, H.-K., Curty, M. & Qi, B. Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012).
  75. Qi, B., Fung, C.-H. F., Lo, H.-K. & Ma, X. Time-shift attack in practical quantum cryptosystems. Quant. Inf. Comp. 7, 7382 (2007).
  76. Zhao, Y., Fung, C.-H. F., Qi, B., Chen, C. & Lo, H.-K. Quantum hacking: experimental demonstration of time-shift attack against practical quantum-key-distribution systems. Phys. Rev. A 78, 042333 (2008).
  77. Makarov, V., Anisimov, A. & Skaar, J. Effects of detector efficiency mismatch on security of quantum cryptosystems. Phys. Rev. A 74, 022313 (2006).
  78. Makarov, V., Anisimov, A. & Skaar, J. Erratum: effects of detector efficiency mismatch on security of quantum cryptosystems [Phys. Rev. A 74, 022313 (2006)]. Phys. Rev. A 78, 019905 (2008).
  79. Lamas-Linares, A. & Kurtsiefer, C. Breaking a quantum key distribution system through a timing side channel. Opt. Express 15, 93889393 (2007).
  80. Lydersen, L. et al. Hacking commercial quantum cryptography systems by tailored bright illumination. Nature Photon. 4, 686689 (2010).
  81. Yuan, Z. L., Dynes, J. F. & Shields, A. J. Avoiding the blinding attack in QKD. Nature Photon. 4, 800801 (2010).
  82. Lydersen, L. et al. Reply to “Avoiding the blinding attack in QKD”. Nature Photon. 4, 801 (2010).
  83. Gerhardt, I. et al. Full-field implementation of a perfect eavesdropper on a quantum cryptography system. Nature Commun. 2, 349 (2011).
  84. Weier, H. et al. Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors. New J. Phys. 13, 073024 (2011).
  85. Jain, N. et al. Device calibration impacts security of quantum key distribution. Phys. Rev. Lett. 107, 110501 (2011).
  86. Xu, F., Qi, B. & Lo, H.-K. Experimental demonstration of phase-remapping attack in a practical quantum key distribution system. New J. Phys. 12, 113026 (2010).
  87. Sun, S.-H., Jiang, M.-S. & Liang, L.-M. Passive Faraday-mirror attack in a practical two-way quantum-key-distribution system. Phys. Rev. A 83, 062331 (2011).
  88. Huang, J.-Z. et al. Quantum hacking on continuous-variable quantum key distribution system using a wavelength attack. Phys. Rev. A 87, 062329 (2013).
  89. Tang, Y.-L. et al. Source attack of decoy-state quantum key distribution using phase information. Phys. Rev. A 88, 022308 (2013).
  90. Jouguet, P., Kunz-Jacques, S. & Diamanti, E. Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution. Phys. Rev. A 87, 062313 (2013).
  91. Tamaki, K., Curty, M., Kato, G., Lo, H.-K. & Azuma, K. Loss-tolerant quantum cryptography with imperfect sources. Preprint at (2013).
  92. Yuan, Z. L., Dynes, J. F. & Shields, A. J. Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography. Appl. Phys. Lett. 98, 231104 (2011).
  93. Lydersen, L., Makarov, V. & Skaar, J. Comment on “Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography”. Appl. Phys. Lett. 99, 196101 (2011).
  94. Yuan, Z. L., Dynes, J. F. & Shields, A. J. Response to “Comment on 'Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography”' Appl. Phys. Lett. 99, 196102 (2011).
  95. Honjo, T. et al. Countermeasure against tailored bright illumination attack for DPS-QKD. Opt. Express 21, 26672673 (2013).
  96. Mayers, D. & Yao, A. Quantum cryptography with imperfect apparatus. in Proc. 39th Ann. Symp. Foundations Comp. Sci. 503509 (IEEE, 1998).
  97. Masanes, L., Pironio, S. & Acín, A. Secure device-independent quantum key distribution with causally in-dependent measurement devices. Nature Commun. 2, 238 (2011).
  98. Reichardt, B. W., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456460 (2013).
  99. Vazirani, U. & Vidick, T. Fully device independent quantum key distribution. Preprint at (2012).
  100. Gisin, N., Pironio, S. & Sangouard, N. Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier. Phys. Rev. Lett. 105, 070501 (2010).
  101. Curty, M. & Moroder, T. Heralded-qubit amplifiers for practical device-independent quantum key distribution. Phys. Rev. A 84, 010304(R)(2011).
  102. Biham, E., Huttner, B. & Mor, T. Quantum cryptographic network based on quantum memories. Phys. Rev. A 54, 26512658 (1996).
  103. Inamori, H. Security of practical time-reversed EPR quantum key distribution. Algorithmica 34, 340365 (2002).
  104. Rubenok, A., Slater, J. A., Chan, P., Lucio-Martinez, I. & Tittel, W. Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks. Phys. Rev. Lett. 111, 130501 (2013).
  105. Ferreira da Silva, T. et al. Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits. Phys. Rev. A 88, 052303 (2013).
  106. Liu, Y. et al. Experimental measurement-device-independent quantum key distribution. Phys. Rev. Lett. 111, 130502 (2013).
  107. Tang, Z. et al. Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution. Phys. Rev. Lett. 112, 190503 (2014).
  108. Briegel, H.-J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 59325935 (1998).
  109. Vernam, G. S. Cipher printing telegraph systems: for secret wire and radio telegraphic communications. J. Am. Inst. Electr. Eng. 45, 109115 (1926).

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Author information

  1. All authors contributed equally to this work.

    • Hoi-Kwong Lo,
    • Marcos Curty &
    • Kiyoshi Tamaki


  1. Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario M5S 3G4, Canada

    • Hoi-Kwong Lo
  2. EI Telecomunicación, Department of Signal Theory and Communications, University of Vigo, E-36310 Vigo, Pontevedra, Spain

    • Marcos Curty
  3. NTT Basic Research Laboratories, NTT Corporation, 3-1, Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan

    • Kiyoshi Tamaki

Competing financial interests

H.-K.L. is a named inventor on US Patent #8,554,814, “Random signal generator using quantum noise” (2013), which is related to the methods described in ref. 59. M.C. is a named inventor on patents and pending patents related to the methods described in refs 57 and 58. K.T. declares no competing financial interests other than his employment with NTT, Basic Research Lab.

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