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.
J. Audretsch and R. Müller, Localized discussion of stimulated processes for Rindler observers and accelerated detectors, Phys. Rev. D 49 (1994) 4056 [INSPIRE].
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.
N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (1984).
S. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Pearson Education, London U.K. (2013).
A. Ferraro, S. Olivares and M. Paris, Gaussian States in Quantum Information, Napoli series on physics and astrophysics, Bibliopolis, Naples Italy (2005).
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].
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].
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).
E.H. Lieb and M.B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 14 (1973) 1938 [INSPIRE].
W. functions site, Modified bessel function of the second kind, http://functions.wolfram.com/Bessel-TypeFunctions/BesselK/06/01/04/01/01/0003/.
G. Arfken and H. Weber, Mathematical methods for physicists, Elsevier Press, Amsterdam the Netherlands (2008).
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.
ArXiv ePrint: 1707.04954
About this article
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
- Black Holes
- Effective Field Theories
- Models of Quantum Gravity