High-dimensional cryptographic quantum parameter estimation

  • Dong Xie
  • Chunling Xu
  • Jianyong Chen
  • An Min Wang


We investigate cryptographic quantum parameter estimation with a high-dimensional system that allows only Bob (Receiver) to access the result and achieve optimal parameter precision from Alice (Sender). Eavesdropper (Eve) only can disturb the parameter estimation of Bob, but she cannot obtain the information of parameter. And Bob can still securely obtain a high-precision estimation of parameter by utilizing the parallel-entangled strategy and sequential strategy with a large repeat count of communication. We analyze the security and show that the high-dimensional system can help to utilize the resource to obtain better precision than the two-dimensional system. Finally, we generalize it to the case of multi-parameter.


Parameter estimation Quantum metrology Quantum communication Quantum cryptography 



This research was supported by the National Natural Science Foundation of China under Grant No. 11747008, Guangxi Natural Science Foundation 2016GXNSFBA380227 and Guangxi Base Promotion Project of Young and Middle-aged Teachers (NO.2017KY0857).


  1. 1.
    Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 68, 557 (1992)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Cheng, W.C., Aritsugi, M.: A user sensitive privacy-preserving location sharing system in mobile social networks. Procedia Comput. Sci. 35, 1692 (2014)CrossRefGoogle Scholar
  4. 4.
    Dowling, J.P.: Quantum optical metrology-the lowdown on high-N00N states. Contemp. Phys. 49, 125 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic, New York (1976)zbMATHGoogle Scholar
  6. 6.
    Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-Enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Farace, A., De Pasquale, A., Adesso, G., Giovannetti, V.: Building versatile bipartite probes for quantum metrology. New J. Phys. 18, 013049 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    Unden, T., Balasubramanian, P., Louzon, D., Vinkler, Y., Plenio, Martin B., Markham, Matthew, Twitchen, Daniel, Lovchinsky, Igor, Sushkov, Alexander O., Lukin, Mikhail D., Retzker, Alex, Naydenov, Boris, Mcguinness, Liam P., Jelezko, Fedor: Quantum metrology enhanced by repetitive quantum error correction. Phys. Rev. Lett. 116, 230502 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    Xie, D., Xu, C., Wang, A.M.: Quantum metrology in coarsened measurement reference. Phys. Rev. A 95, 012117 (2017)ADSCrossRefGoogle Scholar
  11. 11.
    Giovannetti, V., Lloyd, S., Maccone, L.: Positioning and clock synchronization through entanglement. Phys. Rev. A 65, 022309 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced positioning and clock synchronization. Nature 412, 417 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum cryptographic ranging. J. Opt. B Quantum Semiclassical Opt. 4, 413 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    Chiribella, G., Maccone, L., Perinotti, P.: Secret quantum communication of a reference frame. Phys. Rev. Lett. 98, 120501 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Huang, Z., Macchiavello, C., Maccone, L.: Cryptographic quantum metrology. arXiv:1706.03894v1 (2017)
  16. 16.
    Cramér, H.: Mathematical Methods of Statistics. Princeton University, Princeton (1946)zbMATHGoogle Scholar
  17. 17.
    Rao, C.R.: Linear Statistical Inference and Its Applications. Wiley, New York (1973)CrossRefzbMATHGoogle Scholar
  18. 18.
    Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  19. 19.
    Bell, B., Kannan, S., McMillan, A., Clark, A.S., Wadsworth, William J., Rarity, John G.: Multicolor quantum metrology with entangled photons. Phys. Rev. Lett. 111, 093603 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    Joo, J., Munro, W.J., Spiller, T.P.: Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Zhang, L., Chan, K.W.C.: Quantum multiparameter estimation with generalized balanced multimode NOON-like states. Phys. Rev. A 95, 032321 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Liu, N., Cable, H.: Quantum-enhanced multi-parameter estimation for unitary photonic systems. Quantum Sci. Technol. 2, 2 (2017)CrossRefGoogle Scholar
  23. 23.
    Szczykulska, M., Baumgratz, T., Datta, A.: Multi-parameter quantum metrology. Adv. Phys. X 1, 621 (2016)Google Scholar
  24. 24.
    Knott, P.A., Proctor, T.J., Hayes, A.J., Ralph, J.F., Kok, P., Dunningham, J.A.: Local versus global strategies in multiparameter estimation. Phys. Rev. A 94, 062312 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    Young, K.C., Sarovar, M., Kosut, R., Whaley, K.B.: Optimal quantum multiparameter estimation and application to dipole- and exchange-coupled qubits. Phys. Rev. A 79, 062301 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Dorner, U., Demkowicz-Dobrzanski, R., Smith, B., Lundeen, J., Wasilewski, W., Banaszek, K., Walmsley, I.: Optimal quantum phase estimation. Phys. Rev. Lett. 102, 040403 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    Knysh, S.I., Durkin, G.A.: Estimation of Phase and Diffusion: Combining Quantum Statistics and Classical Noise. arXiv:1307.0470 (2013)

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Dong Xie
    • 1
  • Chunling Xu
    • 1
  • Jianyong Chen
    • 1
  • An Min Wang
    • 2
  1. 1.Faculty of ScienceGuilin University of Aerospace TechnologyGuilinPeople’s Republic of China
  2. 2.Department of Modern PhysicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

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