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.

Classical command of quantum systems

Abstract

Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or ‘untrusted’ system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of ‘untrusted’ devices to establish a shared random key, with security based on the validity of quantum physics.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Test for quantumness.
Figure 2: Sub-protocols for verified quantum dynamics.

References

  1. Aharonov, D., Ben-Or, M. & Eban, E. in Proc. Innovations in Computer Science (ICS) (ed. Yao, A.) 453–469 (Tsinghua Univ. Press, 2010)

    Google Scholar 

  2. Broadbent, A., Fitzsimons, J. F. & Kashefi, E. in Proc. IEEE Foundations of Computer Science (FOCS) 517–526 (IEEE Computer Society, 2009)

    Google Scholar 

  3. Bennett, C. H. & Brassard, G. in Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing 175–179 (IEEE Computer Society, 1984)

    Google Scholar 

  4. Lo, H.-K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999)

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Shor, P. W. & Preskill, J. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  6. 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)

    Article  ADS  Google Scholar 

  7. Lydersen, L. et al. Hacking commercial quantum cryptography systems by tailored bright illumination. Nature Photon. 4, 686–689 (2010)

    Article  ADS  CAS  Google Scholar 

  8. Gerhardt, I. et al. Full-field implementation of a perfect eavesdropper on a quantum cryptography system. Nature Commun. 2, 349 (2011)

    Article  ADS  Google Scholar 

  9. Mayers, D. & Yao, A. in Proc. IEEE Foundations of Computer Science (FOCS) 503–509 (IEEE Computer Society, 1998)

    Google Scholar 

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

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  11. Barrett, J., Hardy, L. & Kent, A. No signalling and quantum key distribution. Phys. Rev. Lett. 95, 010503 (2005)

    ADS  PubMed  Google Scholar 

  12. Masanes, L., Renner, R., Christandl, M., Winter, A. & Barrett, J. Unconditional security of key distribution from causality constraints. Preprint at http://arXiv.org/abs/quant-ph/0606049 (2006)

  13. Acín, A., Massar, S. & Pironio, S. Efficient quantum key distribution secure against no-signalling eavesdroppers. N. J. Phys. 8, 126 (2006)

    Article  Google Scholar 

  14. Masanes, L. Universally composable privacy amplification from causality constraints. Phys. Rev. Lett. 102, 140501 (2009)

    Article  ADS  PubMed  Google Scholar 

  15. Hänggi, E., Renner, R. & Wolf, S. in Proc. EUROCRYPT (ed. Gilbert, H.) 216–234 (LNCS 6110, Springer, 2010)

    Google Scholar 

  16. Acín, A. et al. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)

    Article  ADS  PubMed  Google Scholar 

  17. Pironio, S. et al. Device-independent quantum key distribution secure against collective attacks. N. J. Phys. 11, 045021 (2009)

    Article  Google Scholar 

  18. McKague, M. Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices. N. J. Phys. 11, 103037 (2009)

    Article  Google Scholar 

  19. Hänggi, E. & Renner, R. Device-independent quantum key distribution with commuting measurements. Preprint at http://arXiv.org/abs/1009.1833 (2010)

  20. Masanes, L., Pironio, S. & Acín, A. Secure device-independent quantum key distribution with causally independent measurement devices. Nature Commun. 2, 238 (2011)

    Article  ADS  Google Scholar 

  21. Holevo, A. S. Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inf. Transm. 9, 177–183 (1973)

    Google Scholar 

  22. Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)

    Article  MathSciNet  Google Scholar 

  23. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  24. Cirel’son, B. S. Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93–100 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  25. Braunstein, S. L., Mann, A. & Revzen, M. Maximal violation of Bell inequalities for mixed states. Phys. Rev. Lett. 68, 3259–3261 (1992)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  26. Popescu, S. & Rohrlich, D. Which states violate Bell’s inequality maximally? Phys. Lett. A 169, 411–414 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  27. Magniez, F., Mayers, D., Mosca, M. & Ollivier, H. in Proc. Int. Coll. on Automata, Languages and Programming (ICALP) (eds Bugliesi, M. et al.) 72–83 (LNCS 4051, Springer, 2006)

    Book  Google Scholar 

  28. McKague, M., Yang, T. H. & Scarani, V. Robust self-testing of the singlet. J. Phys. A 45, 455304 (2012)

    Article  MathSciNet  Google Scholar 

  29. Miller, C. & Shi, Y. Robust self-testing quantum states and binary nonlocal XOR games. Preprint at http://arXiv.org/abs/1207.1819 (2012)

  30. Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)

    Article  ADS  CAS  Google Scholar 

  31. Watrous, J. PSPACE has constant-round quantum interactive proof systems. Theor. Comput. Sci. 292, 575–588 (2003)

    Article  MathSciNet  Google Scholar 

  32. Fitzsimons, J. F. & Kashefi, E. Unconditionally verifiable blind computation. Preprint at http://arXiv.org/abs/1203.5217 (2012)

  33. Barz, S. et al. Demonstration of blind quantum computing. Science 335, 303–308 (2012)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  34. Broadbent, A., Fitzsimons, J. F. & Kashefi, E. QMIP = MIP*. Preprint at http://arXiv.org/abs/1004.1130 (2010)

  35. Jordan, C. Essai sur la géométrie à n dimensions. Bull. Soc. Math. Fr. 3, 103–174 (1875)

    Article  Google Scholar 

  36. Reichardt, B. W., Unger, F. & Vazirani, U. A classical leash for a quantum system: command of quantum systems via rigidity of CHSH games. Preprint at http://arXiv.org/abs/1209.0448 (2012)

  37. Mossel, E., O'Donnell, R. & Oleszkiewicz, K. Noise stability of functions with low influences: invariance and optimality. Ann. Math. 171, 295–341 (2010)

    Article  MathSciNet  Google Scholar 

  38. McKague, M. Quantum Information Processing with Adversarial Devices. PhD thesis, Univ. Waterloo. (2010)

  39. Gottesman, D. Stabilizer Codes and Quantum Error Correction. PhD thesis, California Inst. Technol. (1997)

  40. Kempe, J., Kobayashi, H., Matsumoto, K. & Vidick, T. Using entanglement in quantum multi-prover interactive proofs. Comput. Complex. 18, 273–307 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank E. Bering, A. Broadbent, A. Chailloux, M. Christandl, R. Colbeck, T. Ito, R. König, M. McKague, V. Madhavan, R. Renner, S. Sondhi and T. Vidick for discussions. Part of this work was conducted while F.U. was at the University of California Berkeley and B.W.R. was at the Institute for Quantum Computing, University of Waterloo. B.W.R. acknowledges support from NSERC, ARO-DTO and Mitacs. U.V. acknowledges support from US NSF grant CCF-0905626 and Templeton grant 21674

Author information

Authors and Affiliations

Authors

Contributions

All authors made significant contributions to the research presented in this paper.

Corresponding author

Correspondence to Ben W. Reichardt.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figure 1 and Supplementary References. (PDF 378 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Reichardt, B., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456–460 (2013). https://doi.org/10.1038/nature12035

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature12035

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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