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High-rate and high-capacity measurement-device-independent quantum key distribution with Fibonacci matrix coding in free space

Abstract

This paper proposes a high-rate and high-capacity measurement-device-independent quantum key distribution (MDI-QKD) protocol with Fibonacci-valued and Lucas-valued orbital angular momentum (OAM) entangled states in free space. In the existing MDI-OAM-QKD protocols, the main encoding algorithm handles encoded numbers in a bit-by-bit manner. To design a fast encoding algorithm, we introduce a Fibonacci matrix coding algorithm, by which, encoded numbers are separated into segments longer than one bit. By doing so, when compared to the existing MDI-OAM-QKD protocols, the new protocol can effectively increase the key rate and the coding capacity. This is because Fibonacci sequences are used in preparing OAM entangled states, reducing the misattribution errors (which slow down the execution cycle of the entire QKD) in QKD protocols. Moreover, our protocol keeps the data blocks as small as possible, so as to have more blocks in a given time interval. Most importantly, our proposed protocol can distill multiple Fibonacci key matrices from the same block of data, thus reducing the statistical fluctuations in the sample and increasing the final QKD rate. Last but not the least, the sender and the receiver can omit classical information exchange and bit flipping in the secure key distillation stage.

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References

  1. 1

    Lai H, Luo M X, Pieprzyk J, et al. An efficient quantum blind digital signature scheme. Sci China Inf Sci, 2017, 60: 082501

  2. 2

    Spedalieri F M. Quantum key distribution without reference frame alignment: exploiting photon orbital angular momentum. Opt Commun, 2006, 260: 340–346

  3. 3

    Li J-L, Wang C. Six-state quantum key distribution using photons with orbital angular momentum. Chin Phys Lett, 2010, 27: 110303

  4. 4

    Zhang C M, Zhu J R, Wang Q. Practical decoy-state reference-frame-independent measurement-device-independent quantum key distribution. Phys Rev A, 2017, 95: 032309

  5. 5

    Allen L, Beijersbergen M W, Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A, 1992, 45: 8185–8189

  6. 6

    Simon D S, Lawrence N, Trevino J, et al. High-capacity quantum Fibonacci coding for key distribution. Phys Rev A, 2013, 87: 032312

  7. 7

    Krenn M, MalikM, ErhardM, et al. Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes. Phil Trans R Soc A, 2017, 375: 20150442

  8. 8

    Bechmann-Pasquinucci H, Peres A. Quantum cryptography with 3-state systems. Phys Rev Lett, 2000, 85: 3313–3316

  9. 9

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

  10. 10

    Lo H K, Curty M, Qi B. Measurement-device-independent quantum key distribution. Phys Rev Lett, 2012, 108: 130503

  11. 11

    Braunstein S L, Pirandola S. Side-channel-free quantum key distribution. Phys Rev Lett, 2012, 108: 130502

  12. 12

    Ma X, Fung C H F, Razavi M. Statistical fluctuation analysis for measurement-device-independent quantum key distribution. Phys Rev A, 2012, 86: 052305

  13. 13

    Tamaki K, Lo H K, Fung C H F, et al. Phase encoding schemes for measurement-device-independent quantum key distribution with basis-dependent flaw. Phys Rev A, 2012, 85: 042307

  14. 14

    Zhang Y C, Li Z, Yu S, et al. Continuous-variable measurement-device-independent quantum key distribution using squeezed states. Phys Rev A, 2014, 90: 052325

  15. 15

    Tang Y-L, Yin H-L, Chen S-J, et al. Field test of measurement-device-independent quantum key distribution. IEEE J Sel Top Quantum Electron, 2015, 21: 116–122

  16. 16

    Ma X, Razavi M. Alternative schemes for measurement-device-independent quantum key distribution. Phys Rev A, 2012, 86: 062319

  17. 17

    Lai H, Luo M X, Zhan C, et al. An improved coding method of quantum key distribution protocols based on Fibonaccivalued OAM entangled states. Phys Lett A, 2017, 381: 2922–2926

  18. 18

    Zhao S M, Gong L Y, Li Y Q, et al. A large-alphabet quantum key distribution protocol using orbital angular momentum entanglement. Chin Phys Lett, 2013, 30: 060305

  19. 19

    Mafu M, Dudley A, Goyal S, et al. Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys Rev A, 2013, 88: 032305

  20. 20

    Wang L, Zhao S M, Gong L Y, et al. Free-space measurement-device-independent quantum-key-distribution protocol using decoy states with orbital angular momentum. Chin Phys B, 2015, 24: 120307

  21. 21

    Chen D, Zhao S H, Shi L, et al. Measurement-device-independent quantum key distribution with pairs of vector vortex beams. Phys Rev A, 2016, 93: 032320

  22. 22

    Da Silva T F, Vitoreti D, Xavier G B, et al. Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits. Phys Rev A, 2013, 88: 052303

  23. 23

    Tang Z, Liao Z, Xu F, et al. Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution. Phys Rev Lett, 2014, 112: 190503

  24. 24

    Pirandola S, Ottaviani C, Spedalieri G, et al. High-rate measurement-device-independent quantum cryptography. Nat Photon, 2015, 9: 397–402

  25. 25

    Vajda S. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. New York: Dover Publications, 2007

  26. 26

    Esmaeili M, Moosavi M, Gulliver T A. A new class of Fibonacci sequence based error correcting codes. Cryptogr Commun, 2017, 9: 379–396

  27. 27

    Yan X, Zhang P F, Zhang J H, et al. Effect of atmospheric turbulence on entangled orbital angular momentum three-qubit state. 2017, 26: 064202

  28. 28

    Fu S, Gao C. Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams. Photon Res, 2016, 4: 1–4

  29. 29

    Jurado-Navas A, Tatarczak A, Lu X, et al. 850-nm hybrid fiber/free-space optical communications using orbital angular momentum modes. Opt Express, 2015, 23: 33721–33732

  30. 30

    Malik M, O’Sullivan M, Rodenburg B, et al. Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding. Opt Express, 2012, 20: 13195–13200

  31. 31

    Ren Y, Huang H, Xie G, et al. Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing. Opt Lett, 2013, 38: 4062–4065

  32. 32

    Rodenburg B, Lavery M P J, Malik M, et al. Influence of atmospheric turbulence on states of light carrying orbital angular momentum. Opt Lett, 2012, 37: 3735–3737

  33. 33

    Huttner B, Imoto N, Gisin N, et al. Quantum cryptography with coherent states. Phys Rev A, 1995, 51: 1863–1869

  34. 34

    Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663

  35. 35

    Lo H K, Ma X, Chen K. Decoy state quantum key distribution. Phys Rev Lett, 2005, 94: 230504

  36. 36

    Fürst M, Weier H, Schmitt-Manderbach T, et al. Free-space quantum key distribution over 144 km. In: Proceedigns of Society of Photo-Optical Instrumentation Engineers (SPIE), Stockholm, 2006. 63990G

  37. 37

    Jiang C, Yu Z W, Wang X B. Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation. Phys Rev A, 2017, 95: 032325

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Acknowledgements

Hong LAI was supported by National Natural Science Foundation of China (Grant No. 61702427), Doctoral Program of Higher Education (Grant No. SWU115091), and financial support in part by 1000-Plan of Chongqing by Southwest University (Grant No. SWU116007). Mingxing LUO was supported by National Natural Science Foundation of China (Grant No. 61772437) and Sichuan Youth Science & Technique Foundation (Grant No. 2017JQ0048). Jun ZHANG was supported by National Natural Science Foundation of China (Grant No. 61401371). Josef PIEPRZYK has been supported by National Science Centre, Poland (Grant No. UMO-2014/15/B/ST6/05130).

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Correspondence to Hong Lai or Mehmet A. Orgun.

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Lai, H., Luo, M., Pieprzyk, J. et al. High-rate and high-capacity measurement-device-independent quantum key distribution with Fibonacci matrix coding in free space. Sci. China Inf. Sci. 61, 062501 (2018). https://doi.org/10.1007/s11432-017-9291-6

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Keywords

  • measurement-device-independent quantum key distribution
  • Fibonacci-matrix coding
  • free space
  • orbital angular momentum
  • bit flipping
  • misattribution errors