Skip to main content

A no-summoning theorem in relativistic quantum theory

Quantum Information Processing volume 12, pages 1023–1032 (2013)Cite this article

Abstract

Alice gives Bob an unknown localized physical state at some point P. At some point Q in the causal future of P, Alice will ask Bob for the state back. Bob knows this, but does not know at which point Q until the request is made. Bob can satisfy Alice’s summons, with arbitrarily short delay, for a quantum state in Galilean space-time or a classical state in Minkowski space-time. However, given an unknown quantum state in Minkowski space-time, he cannot generally fulfil her summons. This no-summoning theorem is a fundamental feature of, and intrinsic to, relativistic quantum theory. It follows from the no-signalling principle and the no-cloning theorem, but not from either alone.

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

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Schrödinger E.: Discussion of probability relations between separated systems. Proc. Cam. Phil. Soc. 555563 (1935); ibid. 446451 (1936)

  2. Bell, J.S.: The theory of local beables. Epistemol. Lett. 9 (1976); reprinted in Dialectica 39, 85–96 (1985) and in [4]

  3. Bell, J.S.: Free variables and local causality. Epistemol. Lett. 15 (1977); reprinted in Dialectica 39, 103–106 (1985) and in [4]

  4. Bell J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)

    MATH  Google Scholar 

  5. 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 

  6. Gisin N.: Weinberg’s non-linear quantum mechanics and supraluminal communications. Phys. Lett. A 143, 1 (1990)

    Article  ADS  Google Scholar 

  7. Gisin N.: Stochastic quantum dynamics and relativity. Helv. Phys. Acta 62, 363 (1989)

    MathSciNet  Google Scholar 

  8. Czachor M.: Mobility and nonseparability. Found. Phys. Lett. 4, 351 (1991)

    Article  MathSciNet  Google Scholar 

  9. Kent A.: Nonlinearity without superluminality. Phys. Rev. A 72, 012108 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  10. Pawlowski M., Paterek T., Kaszlikowski D., Scarani V., Winter A., Zukowski M.: Information causality as a physical principle. Nature 461, 1101 (2009)

    Article  ADS  Google Scholar 

  11. Bennett C.H., Brassard G., Crépeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Wootters W.K., Zurek W.H.: A single quantum cannot be cloned. Nature 299, 802803 (1982)

    Article  Google Scholar 

  13. Dieks D.: Communication by EPR devices. Phys. Lett. A 92(6), 271272 (1982)

    Article  Google Scholar 

  14. Lo H.-K., Chau H.: Is quantum bit commitment really possible?. Phys. Rev. Lett. 78, 3410–3413 (1997)

    Article  ADS  Google Scholar 

  15. Mayers D.: Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78, 3414–3417 (1997)

    Article  ADS  Google Scholar 

  16. D’Ariano G.M., Yuen H.P.: Impossibility of measuring the wave function of a single quantum system. Phys. Rev. Lett. 76, 2832–2835 (1996)

    Article  ADS  Google Scholar 

  17. Yuen H.: Amplification of quantum states and noiseless photon amplifiers. Phys. Lett. A 113, 405–407 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  18. Pati A.K., Braunstein S.L.: Impossibility of deleting an unknown quantum state. Nature 404, 164–165 (2000)

    Article  ADS  Google Scholar 

  19. Barnum H., Caves C.M., Fuchs C.A., Jozsa R., Schumacher B.: Noncommuting mixed states cannot be broadcast. Phys. Rev. Lett. 76, 2818–2821 (1996)

    Article  ADS  Google Scholar 

  20. Lindblad G.: A general no-cloning theorem. Lett. Math. Phys. 47, 189–196 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. Jozsa, R.: A stronger no-cloning theorem. arXiv:quantph/0204153v2

  22. Bužek V., Hillery M.: Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844–1852 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  23. Gisin N., Massar S.: Optimal quntum cloning machines. Phys. Rev. Lett. 79, 2153 (1997)

    Article  ADS  Google Scholar 

  24. Bruss D., Ekert A., Macchiavello C.: Optimal universal quantum cloning and state estimation. Phys. Rev. Lett. 81, 2598 (1998)

    Article  ADS  Google Scholar 

  25. Werner R.F.: Optimal cloning of pure states. Phys. Rev. A 58, 1827 (1998)

    Article  ADS  Google Scholar 

  26. Keyl M., Werner R.F.: Optimal cloning of pure states, testing single clones. J. Math. Phys. 40, 3283 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Kent A., Munro W., Spiller T.: Quantum tagging: authenticating location via quantum information and relativistic signalling constraints. Phys. Rev. A 84, 012326 (2011)

    Article  ADS  Google Scholar 

  28. Buhrman, H., et al.: Position-based quantum cryptography: impossibility and constructions. arXiv:1009.2490v4 (2011)

  29. Vaidman L.: Instantaneous measurement of nonlocal variables. Phys. Rev. Lett. 90(1), 010402 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Malaney, R.: Quantum location verification in noisy channels. arXiv:1004.4689 (2010)

  32. Chandran, N., et al.: Position-based quantum cryptography. arXiv:1005.1750 (2010)

  33. Kent, A., Beausoleil, R., Munro, W., Spiller, T.: Tagging systems US patent US20067075438 (2006)

  34. Kent A.: Secure classical bit commitment using fixed capacity communication channels. J. Cryptol. 18, 313–335 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  35. Braunstein S., Buzek V., Hillery M.: Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit. Phys. Rev. A 63, 052313 (2001)

    Article  ADS  Google Scholar 

  36. Cerf N.: Asymmetric quantum cloning machines in any dimension. J. Mod. Opt. 47, 187 (2000)

    MathSciNet  ADS  Google Scholar 

  37. Fiurasek J., Filip R., Cerf N.: Highly asymmetric quantum cloning in arbitrary dimension. Quant. Inform. Comp. 5, 583 (2005)

    Google Scholar 

  38. Iblisdir S. et al.: Multipartite asymmetric quantum cloning. Phys. Rev. A 72, 042328 (2005)

    Article  ADS  Google Scholar 

  39. Iblisdir, S., Acin, A., Gisin, N.: Generalised asymmetric quantum cloning. quant-ph/0505152 (2005)

  40. Kent A.: Unconditionally secure bit commitment with flying qudits. New J. Phys. 13, 113015 (2011)

    Article  ADS  Google Scholar 

  41. Kent A.: Location-oblivious data transfer with flying entangled qudits. Phys. Rev. A 84, 012328 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    Adrian Kent

  2. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada

    Adrian Kent

Authors
  1. Adrian Kent
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adrian Kent.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kent, A. A no-summoning theorem in relativistic quantum theory. Quantum Inf Process 12, 1023–1032 (2013). https://doi.org/10.1007/s11128-012-0431-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-012-0431-6

Keywords

  • Quantum information
  • Special relativity
  • Quantum cloning
  • Quantum cryptography