Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

A single-qubit position verification protocol that is secure against multi-qubit attacks

Nature Physics volume 18, pages 623–626 (2022)Cite this article

Subjects

Abstract

The position of a device or agent is an important security credential in today’s society, both online and in the real world. Unless in direct proximity, however, the secure verification of a position is impossible without further assumptions. This is true classically1, but also in any future quantum-equipped communications infrastructure2. We show in this work that minimal quantum resources, in the form of a single qubit, combined with classical communication are sufficient to thwart quantum adversaries that pretend to be at a specific position and have the ability to coordinate their action with entanglement. More precisely, we show that adversaries using an increasing amount of entanglement can be combatted solely by increasing the number of classical bits used in the protocol. The presented protocols are noise-robust and within reach of current quantum technology.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Set-up for PV in one spatial dimension (top) and the classical attack (bottom).
Fig. 2: The routing protocol.
Fig. 3: The measuring protocol.
Fig. 4: Attack strategies for the routing and measuring protocols.

Similar content being viewed by others

Data availability

Data sharing is not applicable to this Article as no datasets were generated or analysed during the current study.

References

  1. Chandran, N., Goyal, V., Moriarty, R. & Ostrovsky, R. Position based cryptography. In Proc. Advances in Cryptology—CRYPTO 2009, Lecture Notes in Computer Science (ed. Halevi, S.) Vol. 5677, 391–407 (Springer, 2009).

  2. Buhrman, H. et al. Position-based quantum cryptography: impossibility and constructions. SIAM J. Comput. 43, 150–178 (2014).

    Article  MathSciNet  Google Scholar 

  3. Kent, A., Munro, W. J. & Spiller, T. P. Quantum tagging: authenticating location via quantum information and relativistic signaling constraints. Phys. Rev. A 84, 012326 (2011).

    Article  ADS  Google Scholar 

  4. Malaney, R. A. Location-dependent communications using quantum entanglement. Phys. Rev. A 81, 042319 (2010).

    Article  ADS  Google Scholar 

  5. Vaidman, L. Instantaneous measurement of nonlocal variables. Phys. Rev. Lett. 90, 010402 (2003).

    Article  ADS  Google Scholar 

  6. Beigi, S. & König, R. Simplified instantaneous non-local quantum computation with applications to position-based cryptography. N. J. Phys. 13, 093036 (2011).

    Article  Google Scholar 

  7. Tomamichel, M., Fehr, S., Kaniewski, J. & Wehner, S. A monogamy-of-entanglement game with applications to device-independent quantum cryptography. N. J. Phys. 15, 103002 (2013).

    Article  MathSciNet  Google Scholar 

  8. Ribeiro, J. & Grosshans, F. A tight lower bound for the BB84-states quantum-position-verification protocol. Preprint at https://arxiv.org/abs/1504.07171 (2015).

  9. Lau, H.-K. & Lo, H.-K. Insecurity of position-based quantum-cryptography protocols against entanglement attacks. Phys. Rev. A 83, 012322 (2011).

    Article  ADS  Google Scholar 

  10. Chakraborty, K. & Leverrier, A. Practical position-based quantum cryptography. Phys. Rev. A 92, 052304 (2015).

    Article  ADS  Google Scholar 

  11. Malaney, R. The quantum car. IEEE Wirel. Commun. Lett. 5, 624–627 (2016).

    Article  Google Scholar 

  12. Das, S. & Siopsis, G. Practically secure quantum position verification. N. J. Phys. 23, 063069 (2021).

    Article  MathSciNet  Google Scholar 

  13. Gonzales, A. & Chitambar, E. Bounds on instantaneous nonlocal quantum computation. IEEE Trans. Inf. Theory 66, 2951–2963 (2019).

    Article  MathSciNet  Google Scholar 

  14. Buhrman, H., Fehr, S., Schaffner, C. & Speelman, F. The garden-hose model. In Proc. 4th Conference on Innovations in Theoretical Computer Science ITCS ’13 145–158 (ACM, 2013).

  15. Speelman, F. Instantaneous non-local computation of low T-depth quantum circuits. In Proc. 11th Conference on the Theory of Quantum Computation, Communication and Cryptography TQC 2016, Leibniz International Proceedings in Informatics (LIPIcs) (ed. Broadbent, A.) Vol. 61, 9:1–9:24 (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2016).

  16. Olivo, A., Chabaud, U., Chailloux, A. & Grosshans, F. Breaking simple quantum position verification protocols with little entanglement. Preprint at https://arxiv.org/abs/2007.15808 (2020).

  17. Kent, A. Quantum tagging for tags containing secret classical data. Phys. Rev. A 84, 022335 (2011).

    Article  ADS  Google Scholar 

  18. Gao, F., Liu, B. & Wen, Q.-Y. Enhanced no-go theorem for quantum position verification. Preprint at https://arxiv.org/abs/1305.4254 (2013).

  19. Unruh, D. Quantum position verification in the random oracle model. In Proc. Advances in Cryptology—CRYPTO 2014, Lecture Notes in Computer Science (eds. Garay J.A., Gennaro R.) Vol. 8617, 1–18 (Springer, 2014).

  20. Qi, B. & Siopsis, G. Loss-tolerant position-based quantum cryptography. Phys. Rev. A 91, 042337 (2015).

    Article  ADS  Google Scholar 

  21. Lim, C. C. W. et al. Loss-tolerant quantum secure positioning with weak laser sources. Phys. Rev. A 94, 032315 (2016).

    Article  ADS  Google Scholar 

  22. Allerstorfer, R., Buhrman, H., Speelman, F. & Verduyn Lunel, P. New protocols and ideas for practical quantum position verification. Preprint at https://arxiv.org/abs/2106.12911 (2021).

  23. Junge, M., Kubicki, A. M., Palazuelos, C. & Pérez-García, D. Geometry of Banach spaces: a new route towards position based cryptography. Preprint at https://arxiv.org/abs/2103.16357 (2021).

  24. Renes, J. M. & Boileau, J.-C. Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009).

    Article  ADS  Google Scholar 

  25. Berta, M., Christandl, M., Colbeck, R., Renes, J. M. & Renner, R. The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659–662 (2010).

    Article  Google Scholar 

Download references

Acknowledgements

We thank A. Kent for organizing a workshop on relativistic quantum information theory in February 2020, during which part of this work was presented. A.B. and M.C. acknowledge financial support from the European Research Council (grant agreement no. 81876), VILLUM FONDEN via the QMATH Centre of Excellence (grant no.10059) and the QuantERA ERA-NET Cofund in Quantum Technologies implemented within the European Union’s Horizon 2020 Programme (QuantAlgo project) via the Innovation Fund Denmark.

Author information

Authors and Affiliations

  1. QMATH, Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Andreas Bluhm & Matthias Christandl

  2. QuSoft & Informatics Institute, University of Amsterdam, Amsterdam, Netherlands

    Florian Speelman

Authors
  1. Andreas Bluhm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthias Christandl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Florian Speelman
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to this work.

Corresponding authors

Correspondence to Andreas Bluhm, Matthias Christandl or Florian Speelman.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Carl Miller, Yusuf Alnawakhtha and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Proofs of all statements and discussion.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bluhm, A., Christandl, M. & Speelman, F. A single-qubit position verification protocol that is secure against multi-qubit attacks. Nat. Phys. 18, 623–626 (2022). https://doi.org/10.1038/s41567-022-01577-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01577-0

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing