Skip to main content

Advertisement

SpringerLink
Entangled wavepackets in the vacuum
Download PDF
Download PDF
  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 13 October 2017

Entangled wavepackets in the vacuum

  • Joris Kattemölle  ORCID: orcid.org/0000-0003-0999-01621,2 &
  • Ben Freivogel2,3 

Journal of High Energy Physics volume 2017, Article number: 92 (2017) Cite this article

  • 298 Accesses

  • 1 Altmetric

  • Metrics details

A preprint version of the article is available at arXiv.

Abstract

Motivated by the black hole firewall problem, we find highly entangled pairs of spatially localized modes in quantum field theory. We demonstrate that appropriately chosen wavepackets localized outside the horizon are nearly purified by ‘mirror’ modes behind the horizon. In addition, we calculate the entanglement entropy of a single localized wavepacket in the Minkowski vacuum. In all cases we study, the quantum state of the system becomes pure in the limit that the wavepackets delocalize; we quantify the trade-off between localization and purity.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. J. Audretsch and R. Müller, Localized discussion of stimulated processes for Rindler observers and accelerated detectors, Phys. Rev. D 49 (1994) 4056 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  3. J. Kattemölle, Entanglement in the vacuum and the firewall paradox, MSc Thesis, Universiteit van Amsterdam, Amsterdam the Netherlands (2016), https://esc.fnwi.uva.nl/thesis/centraal/files/f1210881169.pdf.

  4. N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (1984).

  5. S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Pearson Education, London U.K. (2013).

    Google Scholar 

  6. A. Ferraro, S. Olivares and M. Paris, Gaussian States in Quantum Information, Napoli series on physics and astrophysics, Bibliopolis, Naples Italy (2005).

    Google Scholar 

  7. G. Adesso, S. Ragy and A.R. Lee, Continuous variable quantum information: Gaussian states and beyond, Open Syst. Inf. Dyn. 21 (2014) 1440001 [arXiv:1401.4679].

    Article  MathSciNet  MATH  Google Scholar 

  8. T.F. Demarie, Pedagogical introduction to the entropy of entanglement for Gaussian states, arXiv:1209.2748 [INSPIRE].

  9. X.-B. Wang, T. Hiroshima, A. Tomita and M. Hayashi, Quantum information with gaussian states, Phys. Rept. B 448 (2007) 1 [arXiv:0801.4604] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Takagi, Vacuum noise and stress induced by uniform accelerator: Hawking-Unruh effect in Rindler manifold of arbitrary dimensions, Prog. Theor. Phys. Suppl. 88 (1986) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  11. L.C.B. Crispino, A. Higuchi and G.E.A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80 (2008) 787 [arXiv:0710.5373] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. L. Susskind and J. Lindesay, An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe, World Scientific, New York U.S.A. (2005).

    MATH  Google Scholar 

  13. D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys. 88 (2016) 015002 [arXiv:1409.1231] [INSPIRE].

    Article  ADS  Google Scholar 

  14. D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].

  15. D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].

  16. E.H. Lieb and M.B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 14 (1973) 1938 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  17. W. functions site, Modified bessel function of the second kind, http://functions.wolfram.com/Bessel-TypeFunctions/BesselK/06/01/04/01/01/0003/.

  18. G. Arfken and H. Weber, Mathematical methods for physicists, Elsevier Press, Amsterdam the Netherlands (2008).

    MATH  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

  1. QuSoft, CWI, Science Park 123, Amsterdam, The Netherlands

    Joris Kattemölle

  2. Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands

    Joris Kattemölle & Ben Freivogel

  3. GRAPPA, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands

    Ben Freivogel

Authors
  1. Joris Kattemölle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ben Freivogel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joris Kattemölle.

Additional information

ArXiv ePrint: 1707.04954

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kattemölle, J., Freivogel, B. Entangled wavepackets in the vacuum. J. High Energ. Phys. 2017, 92 (2017). https://doi.org/10.1007/JHEP10(2017)092

Download citation

  • Received: 27 July 2017

  • Accepted: 18 September 2017

  • Published: 13 October 2017

  • DOI: https://doi.org/10.1007/JHEP10(2017)092

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Black Holes
  • Effective Field Theories
  • Models of Quantum Gravity
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • California Privacy Statement
  • How we use cookies
  • Manage cookies/Do not sell my data
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.