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arXiv · 1703.00018

Bulk Connectedness and Boundary Entanglement

Ning Bao·Grant N. Remmen
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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.

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Ning Bao, Grant N. Remmen. 2018-05-18. Bulk Connectedness and Boundary Entanglement. https://doi.org/10.1209/0295-5075%2F121%2F60007

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