Skip to main content

Quantum Information Channels in Curved Spacetime

  • Conference paper
Models of Computation in Context (CiE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6735))

Included in the following conference series:

  • 524 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21, 562–564 (1968)

    Article  Google Scholar 

  2. Fulling, S.A.: Nonuniqueness of canonical field quantization in riemannian space-time. Phys. Rev. D 7(10), 2850–2862 (1973)

    Article  Google Scholar 

  3. Davies, P.C.W.: Scalar particle production in schwarzschild and rindler metrics. J. Phys. A 8(4), 609–616 (1975)

    Article  Google Scholar 

  4. Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870–892 (1976)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  6. Bradler, K., Hayden, P., Panangaden, P.: Private communication via the Unruh effect. Journal of High Energy Physics JHEP08(074) (August 2009), doi:10.1088/1126-6708/2009/08/074

    Google Scholar 

  7. Bradler, K., Hayden, P., Panangaden, P.: Quantum communication in Rindler spacetime. Arxiv quant-ph 1007.0997 (July 2010)

    Google Scholar 

  8. Alsing, P.M., Milburn, G.J.: Lorentz invariance of entanglement. Quantum Information and Computation 2, 487 (2002)

    MathSciNet  MATH  Google Scholar 

  9. Alsing, P.M., Milburn, G.J.: Teleportation with a uniformly accelerated partner. Phys. Rev. Lett. 91(18), 180404 (2003)

    Google Scholar 

  10. Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76(1), 93–123 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gingrich, R.M., Adami, C.: Quantum entanglement of moving bodies. Phys. Rev. Lett. 89(27), 270402 (2002)

    Google Scholar 

  12. Caban, P., Rembieliński, J.: Lorentz-covariant reduced spin density matrix and Einstein-Podolsky-Rosen Bohm correlations. Physical Review A 72, 12103 (2005)

    Article  Google Scholar 

  13. Doukas, J., Carson, B.: Entanglement of two qubits in a relativistic orbit. Physical Review A 81(6), 62320 (2010)

    Article  Google Scholar 

  14. Fuentes-Schuller, I., Mann, R.B.: Alice Falls into a Black Hole: Entanglement in Noninertial Frames. Physical Review Letters 95, 120404 (2005)

    Article  MathSciNet  Google Scholar 

  15. Datta, A.: Quantum discord between relatively accelerated observers. Physical Review A 80(5) 80(5), 52304 (2009)

    Article  Google Scholar 

  16. Martin-Martinez, E., León, J.: Quantum correlations through event horizons: Fermionic versus bosonic entanglement. Physical Review A 81(3), 32320 (2010)

    Article  Google Scholar 

  17. Kent, A.: Unconditionally secure bit commitment. Phys. Rev. Lett. 83(7), 1447–1450 (1999)

    Article  Google Scholar 

  18. Czachor, M., Wilczewski, M.: Relativistic Bennett-Brassard cryptographic scheme, relativistic errors, and how to correct them. Physical Review A 68(1), 10302 (2003)

    Article  Google Scholar 

  19. Cliche, M., Kempf, A.: Relativistic quantum channel of communication through field quanta. Physical Review A 81(1), 12330 (2010)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  21. Ahlswede, R., Csiszar, I.: Common randomness in information theory and cryptography. IEEE Transactions on Information Theory 39, 1121–1132 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  22. Cai, N., Winter, A., Yeung, R.W.: Quantum privacy and quantum wiretap channels. Problems of Information Transmission 40(4), 318–336 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Devetak, I.: The private classical capacity and quantum capacity of a quantum channel. IEEE Transactions on Information Theory 51(1), 44–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  24. Schützhold, R., Unruh, W.G.: Comment on Teleportation with a uniformly accelerated partner. arXiv:quant-ph/0506028 (2005)

    Google Scholar 

  25. Kretschmann, D., Werner, R.F.: Tema con variazioni: quantum channel capacity. New Journal of Physics 6, 26-+ (2004)

    Article  Google Scholar 

  26. Hawking, S.W.: Particle creation by black holes. Comm. Math. Phys. 43(3), 199–220 (1975)

    Article  MathSciNet  Google Scholar 

  27. Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1973)

    Book  MATH  Google Scholar 

  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. Hayden, P., Preskill, J.: Black holes as mirrors: Quantum information in random subsystems. Journal of High Energy Physics 0709(120) (2007)

    Google Scholar 

  30. Page, D.: Black hole information. Available on ArXiv hep-th/9305040 (May 1993)

    Google Scholar 

  31. Adami, C., Steeg, G.L.V.: Black holes are almost optimal quantum cloners. arXiv:quant-ph/0601065v1 (January 2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Panangaden, P. (2011). Quantum Information Channels in Curved Spacetime. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21875-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21874-3

  • Online ISBN: 978-3-642-21875-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics