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Do black holes create polyamory?

A preprint version of the article is available at arXiv.


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.


  1. L. Susskind and L. Thorlacius, Hawking radiation and back reaction, Nucl. Phys. B 382 (1992) 123 [hep-th/9203054] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  2. A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. 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].

    ADS  Article  Google Scholar 

  4. V. Coffman, J. Kundu and W.K. Wootters, Distributed entanglement, Phys. Rev. A 61 (2000) 052306 [quant-ph/9907047] [INSPIRE].

  5. M. Koashi and A. Winter, Monogamy of quantum entanglement and other correlations, Phys. Rev. A 69 (2004) 022309 [quant-ph/0310037].

  6. W.K. Wootters and W.H. Zurek, A single quantum cannot be cloned, Nature 299 (1982) 802 [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  7. R.M. Wald, Space, time, and gravity: the theory of the big bang and black holes, University of Chicago Press, U.S.A., (1992).

  8. S. Lloyd and J. Preskill, Unitarity of black hole evaporation in final-state projection models, JHEP 08 (2014) 126 [arXiv:1308.4209] [INSPIRE].

    ADS  Article  Google Scholar 

  9. 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, (2005).

  10. R. Bousso and D. Stanford, Measurements without Probabilities in the Final State Proposal, Phys. Rev. D 89 (2014) 044038 [arXiv:1310.7457] [INSPIRE].

  11. G. ’t Hooft, On the Quantum Structure of a Black Hole, Nucl. Phys. B 256 (1985) 727 [INSPIRE].

  12. G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].

  13. L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

  14. B. Toner et al., Monogamy of Bell correlations and Tsirelson’s bound, quant-ph/0611001.

  15. 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].

    ADS  Article  Google Scholar 

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

  17. 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].

  18. 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].

  19. J. Oppenheim and B. Reznik, Fundamental destruction of information and conservation laws, arXiv:0902.2361 [INSPIRE].

  20. W. Unruh, Decoherence without dissipation, Phil. Trans. A Math. Phys. Eng. Sci. 370 (2012) 4454.

    MathSciNet  Article  MATH  Google Scholar 

  21. 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.

    ADS  Article  Google Scholar 

  22. 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].

    ADS  MathSciNet  Article  Google Scholar 

  23. Y. Aharonov, P.G. Bergmann and J.L. Lebowitz, Time symmetry in the quantum process of measurement, Phys. Rev. 134 (1964) B1410.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  24. D. Harlow, Jerusalem Lectures on Black Holes and Quantum Information, Rev. Mod. Phys. 88 (2016) 015002 [arXiv:1409.1231] [INSPIRE].

  25. D. Dieks, Communication by EPR devices, Phys. Lett. A 92 (1982) 271 [INSPIRE].

  26. D. Gottesman and J. Preskill, Comment on ‘The Black hole final state’, JHEP 03 (2004) 026 [hep-th/0311269] [INSPIRE].

    ADS  Article  Google Scholar 

  27. 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].

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Correspondence to Andrzej Grudka.

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ArXiv ePrint: 1506.07133

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Grudka, A., Hall, M.J.W., Horodecki, M. et al. Do black holes create polyamory?. J. High Energ. Phys. 2018, 45 (2018).

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  • Black Holes
  • Spacetime Singularities