Causality & holographic entanglement entropy

By M. Headrick, V. Hubeny, A. Lawrence, M. Rangamani. 2014

405 citations recorded by the source corpus.

A bstractWe identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

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

View Paper: https://www.semanticscholar.org/paper/9e4fd1144976a479c186ce335c392c4217676612

How researchers see this paper

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

In Astronomy and Astrophysics

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

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

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

Citations in the corpus

• A general proof of the quantum null energy condition (2017, background): “The entanglement wedge is believed to be the largest region containing information reconstructible using operators acting on the sub Hilbert space HA in the QFT [39–42], and so these bulk regions are causally constrained by the boundary theory.”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “In fact there is a general theorem relating C[R] and W [R]: under “reasonable assumptions” such as the null energy condition, global hyperbolicity, etc, we have the containment [6, 9]”
• Inconsistency of islands in theories with long-range gravity (2021, methodology): “We also clarify that we use the phrase “entanglement wedge” according to its original definition [60] so that it is a region of the gravitating spacetime that can be reconstructed from some part of the non-gravitational spacetime.”
• Relative entropy equals bulk relative entropy (2015, background): “RC is generically smaller than Rb [41, 35].”
• Comments on holographic complexity (2016, methodology): “space-like separated from all points in WE [A] [24].”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “This is interesting because black hole horizons always lie at the edge of the causal wedge of the full boundary, while in general the entanglement wedge extends beyond the causal wedge [15,16], and thus beyond the horizon.”
• On entanglement spreading in chaotic systems (2016, background): “(2) Although we have presented this calculation as a second derivation of vB, one can turn the logic around and view these results as a dynamical explanation for a special case of entanglement wedge subregion duality [25, 26, 27].”
• Bit Threads and Holographic Entanglement (2016, background): “Specifically, at order N0 the contribution is given by the EE of the fields in the bulk spatial region r(A) defined by the homology constraint, ∂r(A) = A ∪ m(A) (the so-called “entanglement wedge” [31]).”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “, see the lower panel in figure 8, we are able to recover information about the island with data from the boundary CFT in the corresponding boundary subregion, by applying standard entanglement wedge reconstruction [88–94].”
• Bulk locality from modular flow (2017, background): “The answer should be independent of (10)This suggests that fΠ is a highly singular function especially when any of these null geodesics leaves D(r) along seams that emanate from a caustic (see [5] for some nice pictures of how this happens in a relevant context).”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “A key concept in our current understanding of holographic dualities is the entanglement wedge WA of a bulk spacetime associated with a given region A in the dual holographic field theory [1–3].”
• Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “It is worth emphasizing that if we should indeed understand the factorization as happening at this extremal surface, in order to reconstruct the Wilson line we still need to solve the problem of “entanglement wedge” reconstruction [67–69].”
• Islands in cosmology (2020, methodology): “The encoding is similar to subregion duality in AdS/CFT, where the density matrix of a region on the boundary is encoded in the bulk entanglement wedge [18–20].”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “Returning to the issue of extracting information from the island, entanglement wedge reconstruction [24, 131–137] allows us to recover information about the island with data from the boundary CFT in the corresponding boundary subregion.”
• Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, background): “Yet there has been speculation in the literature that reconstruction should be possible in a larger region, the entanglement wedge [40], see also [41–43].”