Abstract
If quantum gravity does not lead to a breakdown of predictability, then Almheiri-Marolf-Polchinski-Sully (AMPS) have argued that an observer falling into a black hole can perform an experiment which verifies a violation of entanglement monogamy — that late time Hawking radiation is maximally entangled with early time Hawking radiation and also with in-falling radiation — something impossible in quantum field theory. However, as pointed out by Hayden and Harlow, this experiment is infeasible, as the time required to perform the experiment is almost certainly longer than the lifetime of the black hole. Here we propose an alternative firewall experiment which could actually be performed within the black hole’s lifetime. The alternative experiment involves forming an entangled black hole in which the unscrambling of information is precomputed on a quantum memory prior to the creation of the black hole and without acting on the matter which forms the black hole or emerges from it. This would allow an observer near a black hole to signal faster than light. As another application of our precomputing strategy, we show how one can produce entangled black holes which acts like “flat mirrors”, in the sense that information comes out almost instantly (as in the Hayden-Preskill scenario), but also emerge unscrambled, so that it can actually be observed instantly as well. Finally, we prove that a black hole in thermal equilibrium with its own radiation, is uncorrelated with this radiation.
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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:0907.1190v2] [INSPIRE].
S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
S.W. Hawking, The unpredictability of quantum gravity, Commun. Math. Phys. 87 (1982) 395.
J. Preskill, Do black holes destroy information?, hep-th/9209058 [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.
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].
T. Banks, M.E. Peskin and L. Susskind, 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. Roy. Soc. A 370 (2012) 4454
D.N. Page, Is black hole evaporation predictable?, Phys. Rev. Lett. 44 (1980) 301 [INSPIRE].
D. Marolf and J. Polchinski, Gauge-gravity duality and the black hole interior, Phys. Rev. lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].
S.B. Giddings, Nonviolent nonlocality, Phys. Rev. D 88 (2013) 064023 [arXiv:1211.7070] [INSPIRE].
L. Susskind, Singularities, firewalls and complementarity, arXiv:1208.3445 [INSPIRE].
K. Papadodimas and S. Raju, An infalling observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
R. Bousso, Complementarity is not enough, Phys. Rev. D 87 (2013) 124023 [arXiv:1207.5192] [INSPIRE].
T. Jacobson, Boundary unitarity without firewalls, arXiv:1212.6944 [INSPIRE].
D.I. Hwang, B.H. Lee and D.H. Yeom, Is the firewall consistent? Gedanken experiments on black hole complementarity and firewall proposal, JCAP 01 (2013) 005 [arXiv:1210.6733] [INSPIRE].
T. Banks and W. Fischler, No firewalls in holographic space-time or matrix theory, arXiv:1305.3923 [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An apologia for firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, arXiv:1306.0533 [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, arXiv:1306.0622 [INSPIRE].
S.D. Mathur and D. Turton, The flaw in the firewall argument, arXiv:1306.5488 [INSPIRE].
M. Van Raamsdonk, Evaporating firewalls, arXiv:1307.1796 [INSPIRE].
K. Larjo, D.A. Lowe and L. Thorlacius, Black holes without firewalls, Phys. Rev. D 87 (2013) 104018 [arXiv:1211.4620] [INSPIRE].
S. Lloyd and J. Preskill, Unitarity of black hole evaporation in final-state projection models, arXiv:1308.4209 [INSPIRE].
D. Harlow and P. Hayden, Quantum computation vs. firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
L. Susskind, Black hole complementarity and the Harlow-Hayden conjecture, arXiv:1301.4505 [INSPIRE].
B. Unruh, Bohr, Penrose, and Hawking, presented at the Isaac Newton Institute, workshop on quantum gravity and quantum information, December 14, Cambridge, U.K. (2004); http://www.newton.cam.ac.uk/webseminars/pg + ws/2004/qisw05/1214/unruh/.
J. Smolin and J. Oppenheim, Information locking in black holes, Phys. Rev. Lett. 96 (2006) 081302 [hep-th/0507287] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
S.B. Giddings and Y. Shi, Quantum information transfer and models for black hole mechanics, Phys. Rev. D 87 (2013) 064031 [arXiv:1205.4732] [INSPIRE].
M. Horodecki, J. Oppenheim and A. Winter, Partial quantum information, Nature 436 (2005) 673 [quant-ph/0505062].
M. Horodecki, J. Oppenheim and A. Winter, Quantum state merging and negative information, Commun. Math. Phys. 269 (2007) 107 [quant-ph/0512247].
A. Uhlmann, The “transition probability” in the state space of a ∗ -algebra, Rep. Math. Phys. 9 (1976) 273.
W. Unruh and R.M. Wald, Acceleration radiation and generalized second law of thermodynamics, Phys. Rev. D 25 (1982) 942 [INSPIRE].
W.G. Unruh and R.M. Wald, How to mine energy from a black hole, Gen. Rel. Grav. 15 (1983) 195.
A.R. Brown, Tensile strength and the mining of black holes, Phys. Rev. Lett. 111 (2013) 211301 [arXiv:1207.3342] [INSPIRE].
S.W. Hawking, Black holes and thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577.
B. Groisman, S. Popescu and A. Winter, Quantum, classical, and total amount of correlations in a quantum state, Phys. Rev. A 72 (2005) 032317.
P. Hayden, D. Leung, P. Shor, and A. Winter, Randomizing quantum states: constructions and applications, Commun. Math. Phys. 250 (2004) 371 [quant-ph/0307104] [INSPIRE].
C. Dankert, R. Cleve, J. Emerson and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80 (2009) 012304 [quant-ph/0606161].
A. Abeyesinghe, I. Devetak, P. Hayden and A. Winter, The mother of all protocols: restructuring quantum information’s family tree, Roy. Soc. London Proc. Ser. A 465 (2009) 2537 [quant-ph/0606225].
F. Dupuis, M. Berta, J. Wullschleger and R. Renner, One-shot decoupling, arXiv:1012.6044.
B. Schumacher and M. Nielsen, Quantum data processing and error correction, quant-ph/9604022 [INSPIRE].
I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proc. Roy. Soc. A 461 (2005) 207.
M.P. Müller, J. Oppenheim and O.C. Dahlsten, The black hole information problem beyond quantum theory, JHEP 09 (2012) 116 [arXiv:1206.5030] [INSPIRE].
J.F. Clauser, M.A. Horne, A. Shimony and R.A. Holt, Proposed experiment to test local hidden variable theories, Phys. Rev. Lett. 23 (1969) 880 [INSPIRE].
B. Toner et al., Monogamy of Bell correlations and Tsirelson’s bound, quant-ph/0611001 [quant-ph/0611001].
M.M. Wolf, F. Verstraete, M.B. Hastings and J.I. Cirac, Area laws in quantum systems: mutual information and correlations, Phys. Rev. Lett. 100 (2008) 070502 [arXiv:0704.3906] [INSPIRE].
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ArXiv ePrint: 1401.1523
The initial findings of this paper were originally communicated in January 2012, and a presentation of the results is available at http://online.kitp.ucsb.edu/online/fuzzorfire-m13/oppenheim/ (KITP, August 22, 2013).
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Oppenheim, J., Unruh, B. Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle. J. High Energ. Phys. 2014, 120 (2014). https://doi.org/10.1007/JHEP03(2014)120
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DOI: https://doi.org/10.1007/JHEP03(2014)120