Misc,
Multiboundary Wormholes and Holographic Entanglement
(Jun 10, 2014)
Abstract
The AdS/CFT correspondence relates quantum entanglement between boundary
Conformal Field Theories and geometric connections in the dual asymptotically
Anti-de Sitter space-time. 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 AdS\_3 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, in some regions of the moduli space
the entanglement is 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 at least n-1
parties, and that the distillable entanglement between the asymptotic regions
is at least (n+1)/2 partite.
