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Multiboundary wormholes and holographic entanglement.

Balasubramanian, V. and Hayden, P. and Maloney, A. and Marolf, D. and Ross, S. F. (2014) 'Multiboundary wormholes and holographic entanglement.', Classical and quantum gravity., 31 (18). p. 185015.

Abstract

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.

Item Type:Article
Keywords:Holography, Entanglement, Black holes.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1088/0264-9381/31/18/185015
Publisher statement:© 2014 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0264-9381/31/18/185015.
Date accepted:04 August 2014
Date deposited:06 October 2014
Date of first online publication:05 September 2014
Date first made open access:No date available

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