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Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution

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Abstract

We present a security analysis against collective attacks for a time–energy entanglement-based quantum key distribution protocol, given the practical constraints of single-photon detector efficiency, channel loss, and finite-key considerations. We find a positive secure-key capacity when the key length increases beyond \(10^{4}\) for eight-dimensional systems. The minimum key length required is reduced by the ability to post-select on coincident single-photon detection events. Including finite-key effects, we show the ability to establish a shared secret key over a 200 km fiber link.

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References

  1. Bennett, C.H., Brassard, G.: In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing IEEE, New York, pp. 175–179 (1984)

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  3. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Ralph, T.C.: Continuous variable quantum cryptography. Phys. Rev. A 61, 010303 (1999)

    Article  MathSciNet  Google Scholar 

  6. Ralph, T.C.: Security of continuous-variable quantum cryptography. Phys. Rev. A 62, 062306 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  7. Jouguet, P., Kunz-Jacques, S., Leverrier, A., Grangier, P., Diamanti, E.: Experimental demonstration of long-distance continuous-variable quantum key distribution. Nat. Photonics 7(5), 378 (2013)

    Article  ADS  Google Scholar 

  8. Bechmann-Pasquinucci, H., Tittel, W.: Quantum cryptography using larger alphabets. Phys. Rev. A 61, 062308 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)

    Article  ADS  Google Scholar 

  10. Zhang, L., Silberhorn, C., Walmsley, I.A.: Secure quantum key distribution using continuous variables of single photons. Phys. Rev. Lett. 100, 110504 (2008)

    Article  ADS  Google Scholar 

  11. Tittel, W., Brendel, J., Zbinden, H., Gisin, N.: Quantum cryptography using entangled photons in energy-time Bell states. Phys. Rev. Lett. 84, 4737 (2000)

    Article  ADS  Google Scholar 

  12. Thew, R.T., Acín, A., Zbinden, H., Gisin, N.: Bell-type test of energy-time entangled qutrits. Phys. Rev. Lett. 93, 010503 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  13. Ali-Khan, I., Broadbent, C.J., Howell, J.C.: Large-alphabet quantum key distribution using energy-time entangled bipartite states. Phys. Rev. Lett. 98, 060503 (2007)

    Article  ADS  Google Scholar 

  14. Thew, R.T., Tanzilli, S., Tittel, W., Zbinden, H., Gisin, N.: Experimental investigation of the robustness of partially entangled qubits over 11 km. Phys. Rev. A 66, 062304 (2002)

    Article  ADS  Google Scholar 

  15. Qi, B.: Single-photon continuous-variable quantum key distribution based on the energy-time uncertainty relation. Opt. Lett. 31(18), 2795 (2006)

    Article  ADS  Google Scholar 

  16. Mower, J., Zhang, Z., Desjardins, P., Lee, C., Shapiro, J.H., Englund, D.: High-dimensional quantum key distribution using dispersive optics. Phys. Rev. A 87, 062322 (2013)

    Article  ADS  Google Scholar 

  17. Nunn, J., Wright, L.J., Söller, C., Zhang, L., Walmsley, I.A., Smith, B.J.: Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion. Opt. Express 21(13), 15959 (2013)

    Article  ADS  Google Scholar 

  18. Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412(6844), 313 (2001)

    Article  ADS  Google Scholar 

  19. Vaziri, A., Weihs, G., Zeilinger, A.: Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89, 240401 (2002). doi:10.1103/PhysRevLett.89.240401

    Article  ADS  Google Scholar 

  20. Molina-Terriza, G., Vaziri, A., Řeháček, J., Hradil, Z., Zeilinger, A.: Triggered qutrits for quantum communication protocols. Phys. Rev. Lett. 92, 167903 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Zhong, T., Wong, F.N.C., Restelli, A., Bienfang, J.C.: Efficient single-spatial-mode periodically-poled KTiOPO\(_4\) waveguide source for high-dimensional entanglement-based quantum key distribution. Opt. Express 20(24), 26868 (2012)

    Article  ADS  Google Scholar 

  23. Marsili, F., Verma, V.B., Stern, J.A., Harrington, S., Lita, A.E., Gerrits, T., Vayshenker, I., Baek, B., Shaw, M.D., Mirin, R.P., Nam, S.W.: Detecting single infrared photons with 93% system efficiency. Nat. Photonics 7(3), 210 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Scarani, V., Renner, R.: Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing. Phys. Rev. Lett. 100, 200501 (2008). doi:10.1103/PhysRevLett.100.200501

    Article  ADS  Google Scholar 

  26. Sheridan, L., Scarani, V.: Security proof for quantum key distribution using qudit systems. Phys. Rev. A 82, 030301 (2010). doi:10.1103/PhysRevA.82.030301

    Article  ADS  Google Scholar 

  27. Sheridan, L., Scarani, V.: Erratum: Security proof for quantum key distribution using qudit systems. Phys. Rev. A 83, 039901(E) (2011). doi:10.1103/PhysRevA.83.039901

    Article  ADS  Google Scholar 

  28. Cai, R.Y.Q., Scarani, V.: Finite-key analysis for practical implementations of quantum key distribution. New J. Phys. 11, 045024 (2009)

    Article  ADS  Google Scholar 

  29. Sheridan, L., Le, T.P., Scarani, V.: Finite-key security against coherent attacks in quantum key distribution. New J. Phys. 12(12), 123019 (2010)

    Article  ADS  Google Scholar 

  30. Leverrier, A., Grosshans, F., Grangier, P.: Finite-size analysis of a continuous-variable quantum key distribution. Phys. Rev. A 81, 062343 (2010)

    Article  ADS  Google Scholar 

  31. Furrer, F., Franz, T., Berta, M., Leverrier, A., Scholz, V.B., Tomamichel, M., Werner, R.F.: Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks. Phys. Rev. Lett. 109, 100502 (2012)

    Article  ADS  Google Scholar 

  32. Tomamichel, M., Lim, C.C.W., Gisin, N., Renner, R.: Tight finite-key analysis for quantum cryptography. Nat. Commun. 32, 634 (2012)

    Article  Google Scholar 

  33. Leverrier, A., García-Patrón, R., Renner, R., Cerf, N.J.: Security of continuous-variable quantum key distribution against general attacks. Phys. Rev. Lett. 110, 030502 (2013)

    Article  ADS  Google Scholar 

  34. Law, C.K., Eberly, J.H.: Analysis and interpretation of high transverse entanglement in optical parametric down conversion. Phys. Rev. Lett. 92, 127903 (2004)

    Article  ADS  Google Scholar 

  35. Franson, J.D.: Nonlocal cancellation of dispersion. Phys. Rev. A 45, 3126 (1992)

    Article  ADS  Google Scholar 

  36. Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., Sanpera, A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818 (1996)

    Article  ADS  Google Scholar 

  37. Lo, H.K., Chau, H.F., Ardehali, M.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18, 133 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  38. Lodewyck, J., Bloch, M., García-Patrón, R., Fossier, S., Karpov, E., Diamanti, E., Debuisschert, T., Cerf, N.J., Tualle-Brouri, R., McLaughlin, S.W., Grangier, P.: Quantum key distribution over 25 km with an all-fiber continuous-variable system. Phys. Rev. A 76, 042305 (2007)

    Article  ADS  Google Scholar 

  39. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Research Laboratory of Electronics, Masschusetts Institute of Technology, Cambridge, MA, 02139, USA

    Catherine Lee, Jacob Mower, Zheshen Zhang, Jeffrey H. Shapiro & Dirk Englund

  2. Department of Physics, Columbia University, New York, NY, 10027, USA

    Catherine Lee

Authors
  1. Catherine Lee
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  2. Jacob Mower
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  3. Zheshen Zhang
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  4. Jeffrey H. Shapiro
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  5. Dirk Englund
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Corresponding author

Correspondence to Catherine Lee.

Additional information

This work was supported by the DARPA Information in a Photon program, through Grant W911NF-10-1-0416 from the Army Research Office, and the Columbia Optics and Quantum Electronics IGERT under NSF Grant DGE-1069420.

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Lee, C., Mower, J., Zhang, Z. et al. Finite-key analysis of high-dimensional time–energy entanglement-based quantum key distribution. Quantum Inf Process 14, 1005–1015 (2015). https://doi.org/10.1007/s11128-014-0904-x

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  • DOI: https://doi.org/10.1007/s11128-014-0904-x

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