Black hole entanglement and quantum error correction

By Erik P. Verlinde, H. Verlinde. Journal of High Energy Physics, 2012

163 citations recorded by the source corpus.

It was recently argued in [1] that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and do not postulate that the horizon geometry is smooth. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state proposal, and allows a quantitative study of the transition into the “firewall” regime of maximally mixed black hole states.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/43827f0079b51503aed3c359e59de97e4d2e12ee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. D. Stanford
2. D. Harlow
3. S. Raju
4. J. Maldacena
5. S. Shenker
6. L. Susskind
7. Zhenbin Yang
8. Ahmed Almheiri

In Nuclear and High Energy Physics

1. D. Harlow
2. D. Stanford
3. S. Raju
4. J. Maldacena
5. S. Shenker
6. L. Susskind
7. Zhenbin Yang
8. R. Myers

In Statistical and Nonlinear Physics

1. D. Harlow
2. D. Stanford
3. S. Raju
4. J. Maldacena
5. S. Shenker
6. Ahmed Almheiri
7. Zhenbin Yang
8. D. Marolf

Citations in the corpus

• Lessons from the information paradox (2020, methodology): “Subsequently, the construction of the little Hilbert space, as performed about the AdS vacuum, was termed the “code subspace” in [191], following the terminology of [64], and this latter terminology is also commonly adopted in the literature.”
• The Holographic Nature of Null Infinity (2020, background): “This resolution is, of course, not new and the same as the resolution suggested by the ideas of black hole complementarity [44, 45, 46] and ER=EPR [47].”
• An apologia for firewalls (2013, background): “[41, 11] have provided recipes to construct fields behind the horizon of an AdS black hole.”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, background): “We note that such a gauge fixed interpretation allows all of the hallmarks of what is often called state dependence [25–28] and which is naturally associated with the ER=EPR paradigm.”
• Bulk locality and quantum error correction in AdS/CFT (2014, result): “A connection between black holes and quantum error correction was also made in [13], which is essentially an earlier version of the proposal of [11], but again the context was different and our work here should be uncontroversial by comparison.”
• Entanglement wedge reconstruction and the information paradox (2019, background): “The publication of [10] provoked a flood of responses, including [12–17].”
• The holographic entropy cone (2015, background): “This is rather suggestive in view of the recently proposed connections between holography and quantum error correcting codes [33, 49], and it is likely that this observation can be proved for arbitrary n by generalizing the construction of [48].”
• Replica wormholes and the black hole interior (2019, methodology): “ndependent systems, the needed corrections would require a rewall at the horizon. However, if the interior partner is secretly part of the early radiation, then the arguments of [28, 29] do not apply [30, 31, 32, 33, 34]. The ER=EPR proposal [34] suggested that a geometric connection might play a ro”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “Versions of this idea have been proposed in many places [49, 116, 123, 162, 164]; I have recently written a general discussion of what I consider to be the bestdefined of the options, that of Raju and Papadodimas [165–167], and I refer the reader”
• Entwinement and the emergence of spacetime (2014, unknown): “(4)A notion of un-gauging or expanding the Hilbert space and then re-gauging has also appeared in [40, 41], which discuss the problem of seeing behind a horizon in AdS/CFT.”
• Cool horizons for entangled black holes (2013, background): “The connection with error correction was also studied in [35].”