Multiboundary wormholes and holographic entanglement

By Vijay Balasubramanian, Patrick M. Hayden, A. Maloney, D. Marolf, S. Ross. 2014

180 citations recorded by the source corpus.

The AdS/CFT correspondence relates quantum entanglement between boundary conformal field theories and geometric connections in the dual asymptotically anti-de Sitter spacetime. We consider entangled states in the n ?> -fold tensor product of a 1 + 1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, there are regions of the moduli space in which the entanglement is instead almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between all n parties, and that the distillable entanglement between the asymptotic regions is at least ( n + 1 ) / 2 ?> partite.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/967e9893f6e748041f80a93bc362cb7635d97a0e

How researchers see this paper

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

In Geometry and Topology

1. M. Rangamani
2. Michael H. Freedman
3. Hirosi Ooguri
4. M. Headrick
5. A. Hebecker
6. V. Hubeny
7. Eran Palti
8. C. Vafa

In Nuclear and High Energy Physics

1. V. Hubeny
2. D. Harlow
3. M. Rangamani
4. T. Takayanagi
5. R. Myers
6. M. Headrick
7. J. Sully
8. Michael H. Freedman

Citations in the corpus

• Euclidean Wormholes, Baby Universes, and Their Impact on Particle Physics and Cosmology (2018, background): “Interesting extensions include those to multiboundary wormholes [233], to situations with inflating wormhole interiors [234], and many others (see, e.”
• Causality & holographic entanglement entropy (2014, methodology): “This occurs for example in the AdS3-geon spacetimes 15 [34] and in perturbations of the eternal AdS black hole, such as those studied by [35].”
• The holographic entropy cone (2015, methodology): “Such entropies are also realized by random pure states with dimension log di ∝ S(i) [22].”
• Entanglement is not enough (2014, unknown): “The guess is supported by the calculations of Balasubramanian, Hayden,Maloney,Marolf and Ross, [29] where the lack ofGHZ entanglement is explicitly shown for a class of smooth ERBs in (2 + 1)-dimensions.”
• Bit Threads and Holographic Entanglement (2016, background): “This state does not violate any of the known constraints on holographic EEs, and indeed it is has been argued that entanglement of this type occurs in multiboundary black holes [22].”