Quantum Information Channels in Curved Spacetime

  • Prakash Panangaden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6735)

Abstract

Quantum field theory in curved spacetime reveals a fundamental ambiguity in the quantization procedure: the notion of vacuum, and hence of particles, is observer dependent. A state that an inertial observer in Minkowski space perceives to be the vacuum will appear to an accelerating observer to be a thermal bath of radiation. The impact of this Davies-Fulling-Unruh noise on quantum communication has been explored in a recent paper by Bradler, Hayden and the author.

I will review the results of that paper. The problem of quantum communication from an inertial sender to an accelerating observer and private communication between two inertial observers in the presence of an accelerating eavesdropper was studied there. In both cases, they were able to establish compact, tractable formulas for the associated communication capacities assuming encodings that allow a single excitation in one of a fixed number of modes per use of the communications channel. Group theoretical ideas play a key role in the calculation.

I close with a discussion of some issues of quantum communication in curved spacetime that have yet to be understood.

Keywords

Black Hole Quantum Channel Quantum Discord Quantum Communication Achievable Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21, 562–564 (1968)CrossRefGoogle Scholar
  2. 2.
    Fulling, S.A.: Nonuniqueness of canonical field quantization in riemannian space-time. Phys. Rev. D 7(10), 2850–2862 (1973)CrossRefGoogle Scholar
  3. 3.
    Davies, P.C.W.: Scalar particle production in schwarzschild and rindler metrics. J. Phys. A 8(4), 609–616 (1975)CrossRefGoogle Scholar
  4. 4.
    Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870–892 (1976)CrossRefGoogle Scholar
  5. 5.
    Unruh, W.G., Wald, R.M.: What happens when an accelerating observer detects a rindler particle. Phys. Rev. D 29(6), 1047–1056 (1984)CrossRefGoogle Scholar
  6. 6.
    Bradler, K., Hayden, P., Panangaden, P.: Private communication via the Unruh effect. Journal of High Energy Physics JHEP08(074) (August 2009), doi:10.1088/1126-6708/2009/08/074Google Scholar
  7. 7.
    Bradler, K., Hayden, P., Panangaden, P.: Quantum communication in Rindler spacetime. Arxiv quant-ph 1007.0997 (July 2010)Google Scholar
  8. 8.
    Alsing, P.M., Milburn, G.J.: Lorentz invariance of entanglement. Quantum Information and Computation 2, 487 (2002)MathSciNetMATHGoogle Scholar
  9. 9.
    Alsing, P.M., Milburn, G.J.: Teleportation with a uniformly accelerated partner. Phys. Rev. Lett. 91(18), 180404 (2003) Google Scholar
  10. 10.
    Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76(1), 93–123 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gingrich, R.M., Adami, C.: Quantum entanglement of moving bodies. Phys. Rev. Lett. 89(27), 270402 (2002) Google Scholar
  12. 12.
    Caban, P., Rembieliński, J.: Lorentz-covariant reduced spin density matrix and Einstein-Podolsky-Rosen Bohm correlations. Physical Review A 72, 12103 (2005)CrossRefGoogle Scholar
  13. 13.
    Doukas, J., Carson, B.: Entanglement of two qubits in a relativistic orbit. Physical Review A 81(6), 62320 (2010)CrossRefGoogle Scholar
  14. 14.
    Fuentes-Schuller, I., Mann, R.B.: Alice Falls into a Black Hole: Entanglement in Noninertial Frames. Physical Review Letters 95, 120404 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Datta, A.: Quantum discord between relatively accelerated observers. Physical Review A 80(5) 80(5), 52304 (2009)CrossRefGoogle Scholar
  16. 16.
    Martin-Martinez, E., León, J.: Quantum correlations through event horizons: Fermionic versus bosonic entanglement. Physical Review A 81(3), 32320 (2010)CrossRefGoogle Scholar
  17. 17.
    Kent, A.: Unconditionally secure bit commitment. Phys. Rev. Lett. 83(7), 1447–1450 (1999)CrossRefGoogle Scholar
  18. 18.
    Czachor, M., Wilczewski, M.: Relativistic Bennett-Brassard cryptographic scheme, relativistic errors, and how to correct them. Physical Review A 68(1), 10302 (2003)CrossRefGoogle Scholar
  19. 19.
    Cliche, M., Kempf, A.: Relativistic quantum channel of communication through field quanta. Physical Review A 81(1), 12330 (2010)CrossRefGoogle Scholar
  20. 20.
    Maurer, U.M.: The strong secret key rate of discrete random triples. In: Communication and Cryptography – Two Sides of One Tapestry, pp. 271–284. Kluwer Academic Publishers, Dordrecht (1994)CrossRefGoogle Scholar
  21. 21.
    Ahlswede, R., Csiszar, I.: Common randomness in information theory and cryptography. IEEE Transactions on Information Theory 39, 1121–1132 (1993)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Cai, N., Winter, A., Yeung, R.W.: Quantum privacy and quantum wiretap channels. Problems of Information Transmission 40(4), 318–336 (2005)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Devetak, I.: The private classical capacity and quantum capacity of a quantum channel. IEEE Transactions on Information Theory 51(1), 44–55 (2005)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Schützhold, R., Unruh, W.G.: Comment on Teleportation with a uniformly accelerated partner. arXiv:quant-ph/0506028 (2005)Google Scholar
  25. 25.
    Kretschmann, D., Werner, R.F.: Tema con variazioni: quantum channel capacity. New Journal of Physics 6, 26-+ (2004)CrossRefGoogle Scholar
  26. 26.
    Hawking, S.W.: Particle creation by black holes. Comm. Math. Phys. 43(3), 199–220 (1975)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1973)CrossRefMATHGoogle Scholar
  28. 28.
    Hawking, S.W.: Is information lost in black holes? In: Wald, R.M. (ed.) Black Holes and Relativistic Stars, pp. 221–240. University of Chicago Press, Chicago (1998)Google Scholar
  29. 29.
    Hayden, P., Preskill, J.: Black holes as mirrors: Quantum information in random subsystems. Journal of High Energy Physics 0709(120) (2007)Google Scholar
  30. 30.
    Page, D.: Black hole information. Available on ArXiv hep-th/9305040 (May 1993)Google Scholar
  31. 31.
    Adami, C., Steeg, G.L.V.: Black holes are almost optimal quantum cloners. arXiv:quant-ph/0601065v1 (January 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Prakash Panangaden
    • 1
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada
  2. 2.Computing LaboratoryOxford UniversityOxfordUnited Kingdom

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