Journal of High Energy Physics

, 2018:45 | Cite as

Do black holes create polyamory?

  • Andrzej GrudkaEmail author
  • Michael J. W. Hall
  • Michał Horodecki
  • Ryszard Horodecki
  • Jonathan Oppenheim
  • John A. Smolin
Open Access
Regular Article - Theoretical Physics


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.


Black Holes Spacetime Singularities 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Andrzej Grudka
    • 1
    Email author
  • Michael J. W. Hall
    • 2
    • 3
  • Michał Horodecki
    • 4
  • Ryszard Horodecki
    • 4
  • Jonathan Oppenheim
    • 5
    • 6
  • John A. Smolin
    • 7
  1. 1.Faculty of Physics, Adam Mickiewicz UniversityPoznańPoland
  2. 2.Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum DynamicsGriffith UniversityBrisbaneAustralia
  3. 3.Department of Theoretical Physics, Research School of Physics and EngineeringAustralian National UniversityCanberraAustralia
  4. 4.Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and InformaticsUniversity of GdańskGdańskPoland
  5. 5.Department of Physics & AstronomyUniversity College of LondonLondonU.K.
  6. 6.London Interdisciplinary Network for Quantum ScienceLondonU.K.
  7. 7.IBM T.J. Watson Research CenterYorktown HeightsU.S.A.

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