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A no-summoning theorem in relativistic quantum theory


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.

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  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 

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Kent, A. A no-summoning theorem in relativistic quantum theory. Quantum Inf Process 12, 1023–1032 (2013).

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