Abstract
Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. This is because both cloning and non-monogamy also lead to a break-down of the semi-classical causal structure. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. This is due to an interesting duality between temporal correlations and entanglement. A particular example of this is the Horowitz-Maldacena proposal, and we argue that it needn’t lead to cloning or violations of entanglement monogamy. For measurements on systems which appear to be leaving a black hole, we introduce the notion of the temporal product, and argue that it is just as natural a choice for measurements as the tensor product. For black holes, the tensor and temporal products have the same measurement statistics, but result in different type of non-monogamy of correlations, with the former being forbidden in quantum theory while the latter is allowed. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tames the violation of entanglement monogamy.
Article PDF
Similar content being viewed by others
References
L. Susskind and L. Thorlacius, Hawking radiation and back reaction, Nucl. Phys. B 382 (1992) 123 [hep-th/9203054] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S.L. Braunstein, S. Pirandola and K. Życzkowski, Better Late than Never: Information Retrieval from Black Holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
V. Coffman, J. Kundu and W.K. Wootters, Distributed entanglement, Phys. Rev. A 61 (2000) 052306 [quant-ph/9907047] [INSPIRE].
M. Koashi and A. Winter, Monogamy of quantum entanglement and other correlations, Phys. Rev. A 69 (2004) 022309 [quant-ph/0310037].
W.K. Wootters and W.H. Zurek, A single quantum cannot be cloned, Nature 299 (1982) 802 [INSPIRE].
R.M. Wald, Space, time, and gravity: the theory of the big bang and black holes, University of Chicago Press, U.S.A., (1992).
S. Lloyd and J. Preskill, Unitarity of black hole evaporation in final-state projection models, JHEP 08 (2014) 126 [arXiv:1308.4209] [INSPIRE].
C.H. Bennett, Simulated Time Travel, Teleportation without communication, and How to conduct a Romance with Someone who has fallen into a black hole, talk available at http://web.archive.org/web/20070206131550/http://www.research.ibm.com/people/b/bennetc/QUPONBshort.pdf, (2005).
R. Bousso and D. Stanford, Measurements without Probabilities in the Final State Proposal, Phys. Rev. D 89 (2014) 044038 [arXiv:1310.7457] [INSPIRE].
G. ’t Hooft, On the Quantum Structure of a Black Hole, Nucl. Phys. B 256 (1985) 727 [INSPIRE].
G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
B. Toner et al., Monogamy of Bell correlations and Tsirelson’s bound, quant-ph/0611001.
J. Oppenheim and W.G. Unruh, Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle, JHEP 03 (2014) 120 [arXiv:1401.1523] [INSPIRE].
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
T. Banks, L. Susskind and M.E. Peskin, Difficulties for the Evolution of Pure States Into Mixed States, Nucl. Phys. B 244 (1984) 125 [INSPIRE].
W.G. Unruh and R.M. Wald, On evolution laws taking pure states to mixed states in quantum field theory, Phys. Rev. D 52 (1995) 2176 [hep-th/9503024] [INSPIRE].
J. Oppenheim and B. Reznik, Fundamental destruction of information and conservation laws, arXiv:0902.2361 [INSPIRE].
W. Unruh, Decoherence without dissipation, Phil. Trans. A Math. Phys. Eng. Sci. 370 (2012) 4454.
K. Ried, M. Agnew, L. Vermeyden, D. Janzing, R.W. Spekkens and K.J. Resch, A quantum advantage for inferring causal structure, Nature Phys. 11 (2015) 414.
A.J. Leggett and A. Garg, Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?, Phys. Rev. Lett. 54 (1985) 857 [INSPIRE].
Y. Aharonov, P.G. Bergmann and J.L. Lebowitz, Time symmetry in the quantum process of measurement, Phys. Rev. 134 (1964) B1410.
D. Harlow, Jerusalem Lectures on Black Holes and Quantum Information, Rev. Mod. Phys. 88 (2016) 015002 [arXiv:1409.1231] [INSPIRE].
D. Dieks, Communication by EPR devices, Phys. Lett. A 92 (1982) 271 [INSPIRE].
D. Gottesman and J. Preskill, Comment on ‘The Black hole final state’, JHEP 03 (2004) 026 [hep-th/0311269] [INSPIRE].
E. Cohen and M. Nowakowski, Comment on “Measurements without probabilities in the final state proposal”, Phys. Rev. D 97 (2018) 088501 [arXiv:1705.06495] [INSPIRE].
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
Corresponding author
Additional information
ArXiv ePrint: 1506.07133
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Grudka, A., Hall, M.J.W., Horodecki, M. et al. Do black holes create polyamory?. J. High Energ. Phys. 2018, 45 (2018). https://doi.org/10.1007/JHEP11(2018)045
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)045