Bulk Connectedness and Boundary Entanglement

Abstract

We prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surface. We extend this no-go theorem to general, arbitrary partitions of the boundary manifolds into non-clopen parts, proving that the density matrix cannot be a tensor product. This result gives a necessary condition for states to potentially correspond to holographic duals.

12 pages, 2 figures

References in corpus (6)

• Holography from Conformal Field Theory
• Notes on Some Entanglement Properties of Quantum Field Theory
• The Holographic Entropy Cone
• Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality
• Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes
• Boundary States as Holographic Duals of Trivial Spacetimes

Cited by in corpus (4)

• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Area Law Unification and the Holographic Event Horizon
• Wormhole Traversability via Quantum Random Walks
• Black Hole Complementarity and ER/EPR