Bulk locality and quantum error correction in AdS/CFT

By Ahmed Almheiri, Xi Dong, D. Harlow. 2014

817 citations recorded by the source corpus.

A bstractWe point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a “quantum secret sharing scheme”, and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard “operator algebra quantum error correction” of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of “subregion-subregion” duality in AdS/CFT, and clarifies the limits of its validity.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cf1b2235d7ed491870a2448c443803c73586d2a8

How researchers see this paper

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

In Nuclear and High Energy Physics

1. D. Harlow
2. S. Raju
3. R. Myers
4. D. Stanford
5. J. Maldacena
6. T. Takayanagi
7. V. Hubeny
8. Thomas Hartman

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. D. Stanford
4. R. Myers
5. J. Maldacena
6. Thomas Hartman
7. V. Hubeny
8. Ahmed Almheiri

Citations in the corpus

• Emergent Gravity and the Dark Universe (2016, background): “These networks are designed so that they describe an encoding map from the ‘logical’ bulk states onto the Hilbert space of ‘physical’ boundary states [39].”
• Islands outside the horizon (2019, result): “This is similar to the situation discussed in [27].”
• Relative entropy equals bulk relative entropy (2015, background): “In particular, it can help answer the question of whether the boundary region R describes the entanglement wedge or only the causal wedge [32, 33, 34, 35].”
• 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].”
• Holographic Entanglement Entropy (2016, methodology): “other compelling reasons to believe in the entanglement wedge reconstruction conjecture as was originally argued using ideas borrowed from quantum error correction by Almheiri, Dong, and Harlow (ADH) [173] and beautifully illustrated in toy models built using tensor networks [174] (which has come to”
• Integral geometry and holography (2015, background): “Other recent work on bulk reconstruction includes [59–62].”
• A stereoscopic look into the bulk (2016, background): “For some readers, this may sound similar to the story of bulk operators and error correction [30].”
• Harnessing the Power of the Second Quantum Revolution (2020, background): “This extends to new descriptions of space-time itself and the famous anti–de Sitter space – conformal field theory (AdS-CFT) correspondence in quantum gravity and string theory, which has the structure of a quantum error-correcting code [149].”
• Holographic duality from random tensor networks (2016, background): “These codes simultaneously satisfies several desired properties, including the RT formula for a subset of boundary states, error correction properties of bulk local operators [9], a kind of bulk gauge invariance, and the possibility of sub-AdS locality.”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, methodology): “Since the last step of this proof is a bit complicated, it is worth mentioning that there is a simple proof [1] that (4) ⇒ (2): we observe that (4) implies that OR acts within the subspace ofHRA that appears with nonzero coefficients in the Schmidt decomposition of |φ〉 into RA and A.”
• The AdS/CFT correspondence (2014, background): “For example, following up on the suggested connections [162] between the distance from the horizon to computational complexity, [163] relates the radial bulk direction to a measure of how well”
• Bulk locality from modular flow (2017, methodology): “However, if we wanted to use the formulas of [6, 12] in this bulk perturbative setting, their interpretation would be that they make the extrapolate dictionary more precise.”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “The physics in the wedge WA can then be reconstructed from field theory degrees of freedom in A [6–9].”
• Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
• Diffeomorphism-invariant observables and their nonlocal algebra (2015, background): “In particular, one can likewise construct Wilson line operators, associated with “Fefferman-Graham” gauge, there; for related discussion see [16, 18, 36].”
• Statistical mechanics of quantum error correcting codes (2020, background): “[12] Ahmed Almheiri, Xi Dong, and Daniel Harlow, “Bulk locality and quantum error correction in AdS/CFT,” Journal of High Energy Physics 2015, 163 (2015), arXiv:1411.”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “The regime of validity of this construction of local bulk fields has recently been reinterpreted in the language of quantum error correction, a beautiful subject that is unfortunately beyond the scope of these notes [106, 107].”