Advertisement

Unitarity of black hole evaporation in final-state projection models

  • Seth Lloyd
  • John PreskillEmail author
Open Access
Article

Abstract

Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.

Keywords

Black Holes Spacetime Singularities 

Notes

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.

References

  1. [1]
    S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].ADSMathSciNetGoogle Scholar
  3. [3]
    L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].ADSMathSciNetGoogle Scholar
  4. [4]
    L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].
  6. [6]
    L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  8. [8]
    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. [10]
    D.N. Page, Black hole information, hep-th/9305040 [INSPIRE].
  11. [11]
    B.M. Terhal, Is entanglement monogamous?, IBM J. Res. Dev. 48 (2004) 71 [quant-ph/0307120].CrossRefGoogle Scholar
  12. [12]
    M. Koashi and A. Winter, Monogamy of quantum entanglement and other correlations, Phys. Rev. A 69 (2004) 022309 [quant-ph/0310037].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    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].ADSCrossRefGoogle Scholar
  15. [15]
    J. Preskill, private communication at the ITP, UC Santa Barbara Conference on Quantum Aspects of Black Holes, 21-26 Jun 1993.Google Scholar
  16. [16]
    P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An apologia for firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S.B. Giddings, Nonviolent nonlocality, Phys. Rev. D 88 (2013) 064023 [arXiv:1211.7070] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    K. Papadodimas and S. Raju, An infalling observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    E. Verlinde and H. Verlinde, Black hole entanglement and quantum error correction, JHEP 10 (2013) 107 [arXiv:1211.6913] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortschr. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  22. [22]
    G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    W.K. Wootters and W.H. Zurek, A single quantum cannot be cloned, Nature 299 (1982) 802 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    D. Dieks, Communication by EPR devices, Phys. Lett. A 92 (1982) 271 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].ADSMathSciNetGoogle Scholar
  26. [26]
    D. Gottesman and J. Preskill, Comment onThe black hole final state’, JHEP 03 (2004) 026 [hep-th/0311269] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    S. Lloyd, Almost certain escape from black holes, Phys. Rev. Lett. 96 (2006) 061302 [quant-ph/0406205] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    Y. Aharonov, D.Z. Albert and L. Vaidman, How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett. 60 (1988) 1351 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S. Lloyd et al., Closed timelike curves via post-selection: theory and experimental demonstration, Phys. Rev. Lett. 106 (2011) 040403 [arXiv:1005.2219] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Lloyd, L. Maccone, R. Garcia-Patron, V. Giovannetti and Y. Shikano, Quantum mechanics of time travel through post-selected telportation, Phys. Rev. D 84 (2011) 025007 [arXiv:1007.2615].ADSGoogle Scholar
  31. [31]
    D. Harlow and P. Hayden, Quantum computation vs. firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    R. Bousso, Complementarity is not enough, Phys. Rev. D 87 (2013) 124023 [arXiv:1207.5192] [INSPIRE].ADSGoogle Scholar
  33. [33]
    R. Bousso and D. Stanford, Measurements without probabilities in the final state proposal, Phys. Rev. D 89 (2014) 044038 [arXiv:1310.7457] [INSPIRE].ADSGoogle Scholar
  34. [34]
    M. Rangamani and M. Rota, Quantum channels in quantum gravity, arXiv:1405.4710 [INSPIRE].
  35. [35]
    C.H. Bennett et al., Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 (1993) 1895 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  36. [36]
    E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D 41 (1990) 1796 [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    M. Żukowski, A. Zeilinger, M.A. Horne and A.K. Ekert, “Event-ready-detectorsBell experiment via entanglement swapping, Phys. Rev. Lett. 71 (1993) 4287.ADSCrossRefGoogle Scholar
  39. [39]
    S. Bose, V. Vedral and P.L. Knight, A multiparticle generalization of entanglement swapping, Phys. Rev. A 57 (1998) 822 [quant-ph/9708004] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    D. Marolf and J. Polchinski, Gauge/gravity duality and the black hole interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    P. Hayden, M. Horodecki, A. Winter and J. Yard, A decoupling approach to the quantum capacity, Open Syst. Inf. Dyn. 15 (2008) 7 [quant-ph/0702005].CrossRefzbMATHMathSciNetGoogle Scholar
  42. [42]
    C. Dankert, R. Cleve, J. Emerson and E. Livine, Exact and approximate unitary 2-designs: constructions and applications, Phys. Rev. A 80 (2009) 012304 [quant-ph/0606161].ADSCrossRefGoogle Scholar
  43. [43]
    J. Polchinski, L. Susskind and N. Toumbas, Negative energy, superluminosity and holography, Phys. Rev. D 60 (1999) 084006 [hep-th/9903228] [INSPIRE].ADSMathSciNetGoogle Scholar
  44. [44]
    S. Aaronson, Quantum computing, postselection, and probabilistic polynomial-time, Proc. Roy. Soc. A 461 (2005) 3473 [quant-ph/0412187].ADSCrossRefMathSciNetGoogle Scholar
  45. [45]
    R. Bousso, Firewalls from double purity, Phys. Rev. D 88 (2013) 084035 [arXiv:1308.2665] [INSPIRE].ADSGoogle Scholar
  46. [46]
    R. Bousso, Frozen vacuum, Phys. Rev. Lett. 112 (2014) 041102 [arXiv:1308.3697] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMITCambridgeU.S.A.
  2. 2.Institute for Quantum Information and Matter, CaltechPasadenaU.S.A.

Personalised recommendations