Remote State Preparation for Quantum Fields

Abstract

Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the Reeh–Schlieder theorem, that it is possible for relativistic quantum field theories, and a “physical” process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with non-relativistic fields, and show that remote state preparation is also possible for them, hence obtaining a Reeh–Schlieder-like result for general fields. Interestingly, in the nonrelativistic case, the process may rely on completely different resources than the ones used in the relativistic case.

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Fig. 1

Notes

  1. 1.

    Note that \(\mathcal {N}_2\) is, as required, symmetric to exchange of \({\mathbf {x}}\) and \({\mathbf {y}}\).

  2. 2.

    For some desired states, a finite T will only be achieved at the cost of an additional infidelity. This infidelity could be made arbitrarily small.

  3. 3.

    This feature ‘protects’ causality. Without it, one could have used this process for signalling.

References

  1. 1.

    Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2.

    Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)

    ADS  Article  Google Scholar 

  3. 3.

    Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    ADS  Article  Google Scholar 

  4. 4.

    Reeh, H., Schlieder, S.: Bemerkungen zur Unitäräquivalenz von lorentzinvarianten Feldern. Nuovo Cim. 22, 1051 (1961)

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Schlieder, S.: Some remarks about the localization of states in a quantum field theory. Commun. Math. Phys. 1, 265 (1965)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Haag, R.: Local Quantum Physics: Fields. Algebras, Texts and Monographs in Physics Springer, Particles (1996). ISBN 9783540610496

  7. 7.

    Ber, R., Kenneth, O., Reznik, B.: Superoscillations underlying remote state preparation for relativistic fields. Phys. Rev. A 91, 052312 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)

    ADS  Article  Google Scholar 

  9. 9.

    Berry, M.: Celebration of the 60th Birthday of Yakir Aharonov. World Scientific, Singapore, pp. 55–65 (1994a)

  10. 10.

    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Flanders, H.: Differential Forms with Applications to the Physical Sciences. Dover Publications, Mineola (1989)

  13. 13.

    Berry, M.: Evanescent and real waves in quantum billiards and Gaussian beams. J. Phys. A 27, L391 (1994b)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Reznik, B.: Trans-Planckian tail in a theory with a cutoff. Phys. Rev. D 55, 2152 (1997)

    ADS  Article  Google Scholar 

  15. 15.

    Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists: A Comprehensive Guide. Academic Press (2012)

  16. 16.

    Clifton, R., Feldman, D.V., Halvorson, H., Redhead, M.L., Wilce, A.: Superentangled states. Phys. Rev. A 58, 135 (1998)

    ADS  Article  Google Scholar 

  17. 17.

    Verch, R., Werner, R.F.: Distillability and positivity of partial transposes in general quantum field systems. Rev. Math. Phys. 17, 545 (2005)

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Peskin, M.E., Schroeder, D.V.: An Introduction To Quantum Field Theory. Westview Press (1995)

  19. 19.

    Hegerfeldt, G.: Remark on causality and particle localization. Phys. Rev. D 10, 3320 (1974)

    ADS  Article  Google Scholar 

  20. 20.

    Hegerfeldt, G., Ruijsenaars, S.: Remarks on causality, localization, and spreading of wave packets. Phys. Rev. D 22, 377 (1980)

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    Hegerfeldt, G.: Causality problems for Fermi’s two-atom system. Phys. Rev. Lett. 72, 596 (1994)

    ADS  Article  MATH  Google Scholar 

  22. 22.

    Petrosky, T., Ordonez, G., Prigogine, I.: Quantum transitions and nonlocality. Phys. Rev. A 62, 042106 (2000)

    ADS  Article  Google Scholar 

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Acknowledgments

The authors wish to thank B. Reznik and O. Kenneth for helpful discussions. EZ acknowledges the support of the Alexander-von-Humboldt foundation.

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Correspondence to Ran Ber.

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Ber, R., Zohar, E. Remote State Preparation for Quantum Fields. Found Phys 46, 804–814 (2016). https://doi.org/10.1007/s10701-016-0001-3

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Keywords

  • Remote state preparation
  • Quantum fields
  • Superoscillations
  • Reeh-Schlieder theorem