Abstract
In the Hayden-Preskill thought experiment, the Hawking radiation emitted before a quantum state is thrown into the black hole is used along with the radiation collected later for the purpose of decoding the quantum state. A natural question is how the recoverability is affected if the stored early radiation is damaged or subject to decoherence, and/or the decoding protocol is imperfectly performed. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
A. Abeyesinghe, I. Devetak, P. Hayden and A. Winter, The mother of all protocols: restructuring quantum information’s family tree, Proc. Roy. Soc. A 465 (2009) 2537 [quant-ph/0606225].
P. Hayden, M. Horodecki, A. Winter and J. Yard, A decoupling approach to the quantum capacity, Open Syst. Info. Dyn. 15 (2008) 7 [quant-ph/0702005].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
B. Yoshida and A. Kitaev, Efficient decoding for the Hayden-Preskill protocol, arXiv:1710.03363 [INSPIRE].
B. Yoshida and N.Y. Yao, Disentangling Scrambling and Decoherence via Quantum Teleportation, Phys. Rev. X 9 (2019) 011006 [arXiv:1803.10772] [INSPIRE].
B. Yoshida, Soft mode and interior operator in the Hayden-Preskill thought experiment, Phys. Rev. D 100 (2019) 086001 [arXiv:1812.07353] [INSPIRE].
P. Gao, D.L. Jafferis and A.C. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the Fast Scrambling Conjecture, JHEP 04 (2013) 022 [arXiv:1111.6580] [INSPIRE].
P. Hosur, X.-L. Qi, D.A. Roberts and B. Yoshida, Chaos in quantum channels, JHEP 02 (2016) 004 [arXiv:1511.04021] [INSPIRE].
D.A. Roberts and B. Yoshida, Chaos and complexity by design, JHEP 04 (2017) 121 [arXiv:1610.04903] [INSPIRE].
A. Nahum, J. Ruhman, S. Vijay and J. Haah, Quantum Entanglement Growth Under Random Unitary Dynamics, Phys. Rev. X 7 (2017) 031016 [arXiv:1608.06950] [INSPIRE].
C. von Keyserlingk, T. Rakovszky, F. Pollmann and S. Sondhi, Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws, Phys. Rev. X 8 (2018) 021013 [arXiv:1705.08910] [INSPIRE].
J. Cotler, N. Hunter-Jones, J. Liu and B. Yoshida, Chaos, Complexity, and Random Matrices, JHEP 11 (2017) 048 [arXiv:1706.05400] [INSPIRE].
V. Khemani, A. Vishwanath and D.A. Huse, Operator spreading and the emergence of dissipation in unitary dynamics with conservation laws, Phys. Rev. X 8 (2018) 031057 [arXiv:1710.09835] [INSPIRE].
B. Yoshida, Firewalls vs. Scrambling, JHEP 10 (2019) 132 [arXiv:1902.09763] [INSPIRE].
J. Kudler-Flam, M. Nozaki, S. Ryu and M.T. Tan, Quantum vs. classical information: operator negativity as a probe of scrambling, JHEP 01 (2020) 031 [arXiv:1906.07639] [INSPIRE].
J. Kudler-Flam, M. Nozaki, S. Ryu and M.T. Tan, Entanglement of Local Operators and the Butterfly Effect, arXiv:2005.14243 [INSPIRE].
B. Yan and N.A. Sinitsyn, Recovery of damaged information and the out-of-time-ordered correlators, Phys. Rev. Lett. 125 (2020) 040605 [arXiv:2003.07267] [INSPIRE].
L. Piroli, C. Sünderhauf and X.-L. Qi, A Random Unitary Circuit Model for Black Hole Evaporation, JHEP 04 (2020) 063 [arXiv:2002.09236] [INSPIRE].
K.A. Landsman et al., Verified Quantum Information Scrambling, Nature 567 (2019) 61 [arXiv:1806.02807] [INSPIRE].
N. Bao, S.M. Carroll, A. Chatwin-Davies, J. Pollack and G.N. Remmen, Branches of the Black Hole Wave Function Need Not Contain Firewalls, Phys. Rev. D 97 (2018) 126014 [arXiv:1712.04955] [INSPIRE].
K. Agarwal and N. Bao, Toy model for decoherence in the black hole information problem, Phys. Rev. D 102 (2020) 086017 [arXiv:1912.09491] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
Z. Webb, The clifford group forms a unitary 3-design, arXiv:1510.02769.
Y. Li, X. Chen and M.P.A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B 98 (2018) 205136 [arXiv:1808.06134] [INSPIRE].
Y. Li, X. Chen and M.P.A. Fisher, Measurement-driven entanglement transition in hybrid quantum circuits, Phys. Rev. B 100 (2019) 134306 [arXiv:1901.08092] [INSPIRE].
B. Skinner, J. Ruhman and A. Nahum, Measurement-Induced Phase Transitions in the Dynamics of Entanglement, Phys. Rev. X 9 (2019) 031009 [arXiv:1808.05953] [INSPIRE].
R. Vasseur, A.C. Potter, Y.-Z. You and A.W.W. Ludwig, Entanglement Transitions from Holographic Random Tensor Networks, Phys. Rev. B 100 (2019) 134203 [arXiv:1807.07082] [INSPIRE].
A. Zabalo, M.J. Gullans, J.H. Wilson, S. Gopalakrishnan, D.A. Huse and J.H. Pixley, Critical properties of the measurement-induced transition in random quantum circuits, Phys. Rev. B 101 (2020) 060301 [arXiv:1911.00008] [INSPIRE].
Y. Bao, S. Choi and E. Altman, Theory of the phase transition in random unitary circuits with measurements, Phys. Rev. B 101 (2020) 104301 [arXiv:1908.04305] [INSPIRE].
S. Choi, Y. Bao, X.-L. Qi and E. Altman, Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition, Phys. Rev. Lett. 125 (2020) 030505 [arXiv:1903.05124] [INSPIRE].
M.J. Gullans and D.A. Huse, Scalable probes of measurement-induced criticality, Phys. Rev. Lett. 125 (2020) 070606 [arXiv:1910.00020] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.13493
Rights and permissions
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.
About this article
Cite this article
Bao, N., Kikuchi, Y. Hayden-Preskill decoding from noisy Hawking radiation. J. High Energ. Phys. 2021, 17 (2021). https://doi.org/10.1007/JHEP02(2021)017
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)017