Causal holographic information

By V. Hubeny, M. Rangamani. 2012

221 citations recorded by the source corpus.

A bstractWe propose a measure of holographic information based on a causal wedge construction. The motivation behind this comes from an attempt to understand how boundary field theories can holographically reconstruct spacetime. We argue that given the knowledge of the reduced density matrix in a spatial region of the boundary, one should be able to reconstruct at least the corresponding bulk causal wedge. In attempt to quantify the ‘amount of information’ contained in a given spatial region in field theory, we consider a particular bulk surface (specifically a co-dimension two surface in the bulk spacetime which is an extremal surface on the boundary of the bulk causal wedge), and propose that the area of this surface, measured in Planck units, naturally quantifies the information content. We therefore call this area the causal holographic information. We also contrast our ideas with earlier studies of holographic entanglement entropy. In particular, we establish that the causal holographic information, whilst not being a von Neumann entropy, curiously enough agrees with the entanglement entropy in all cases where one has a microscopic understanding of entanglement entropy.

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

View Paper: https://www.semanticscholar.org/paper/9546e69b9ccd87422c8cffa3d169836cba4318ec

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. V. Hubeny
4. J. Maldacena
5. D. Stanford
6. T. Takayanagi
7. S. Raju
8. M. Rangamani

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

1. D. Harlow
2. R. Myers
3. S. Raju
4. D. Stanford
5. J. Maldacena
6. Aitor Lewkowycz
7. T. Takayanagi
8. Ahmed Almheiri

Citations in the corpus

• Deriving covariant holographic entanglement (2016, background): “, one can use causal structures to motivate a different construction leading to the causal holographic information [4].”
• Entwinement and the emergence of spacetime (2014, unknown): “In fact, method (1) applies only in spacetimes where entanglement entropies agree with causal holographic information [6, 56, 65].”
• Causality & holographic entanglement entropy (2014, background): “Partial progress towards this result was achieved in [22, 23], which showed that the extremal surface EA generically lies outside of the “causal wedge” of D[A], the intersection of the bulk causal future and causal past of D[A].”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “• Subregion Duality: Given a subregion A of a boundary time-slice Σ, we are able to reconstruct any bulk operator φ(x) which is in the causal wedge of A, denoted CA and defined as the intersection of the bulk future and the bulk past of the boundary domain of dependence of A, as a CFT operator with ”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “There is an elegant covariant description of these generalized AdS-Rindler wedges, which can be stated for an arbitrary boundary spatial subregion as follows [52]:”
• Bulk locality and quantum error correction in AdS/CFT (2014, background): “The causal wedge of a CFT subregion A [10] is defined as WC [A] ≡ J [D[A]] ∩ J −[D[A]].”
• Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “In the classical case, it is known that the extremal surfaces XR do not intersect the causal wedge WR = I (DR) ∩ I(DR) associated with the domain of dependence DR of a boundary region R, on any spacetime obeying the null energy condition [22, 23].”
• Relative entropy equals bulk relative entropy (2015, background): “There is another bulk region one can associate to R, the causal wedge (with spacelike slice RC) which is the set of all bulk points in causal contact with D[R], [40].”
• Entanglement entropy from a holographic viewpoint (2012, background): “Moreover, quite recently, there have been interesting discussions on reconstructions of the bulk geometry from the information on a certain region at the boundary [192, 193, 194].”
• Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy (2012, background): “w A Area[ ( )] might be a coarse-grained measure of the entropy in A, as proposed in [13, 39].”
• Islands outside the horizon (2019, background): “4 See also [15, 16] for the corresponding argument for (3)Recall that our discussion is valid when b′ < φr, so we need c 1 and φ0/c not too large.”
• Bulk curves from boundary data in holography (2013, background): “is tangent to the bulk circle we started with. This re ects a relation between entanglement entropy and causal holographic information that holds in the vacuum of two dimensional holographic theories [23], but not in general settings such as excited states in higher dimensions. The result (25) immed”
• Integral geometry and holography (2015, background): “Other recent work on bulk reconstruction includes [59–62].”
• The AdS/CFT correspondence (2014, background): “or an eective grav63 In fact, an even simpler construct is the ‘causal wedge’ (which only depends on the bulk causal structure) and associated quantities such as the ‘causal holographic information’ [166]. However, the corresponding objects in the CFT dual are yet to be identied. { 42 { itational de”
• On entanglement spreading in chaotic systems (2016, background): “Other proposals have been made for the bulk region that is described by a given boundary region, including the “causal wedge” [25, 28, 30].”
• The gravity dual of a density matrix (2012, background): “We also became aware of [9], which considers related questions.”