Surface/state correspondence as a generalized holography

Abstract

We propose a new duality relation between codimension-two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on the existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of anti-de Sitter space/conformal field theory (AdS/CFT) in terms of the tensor networks, so-called MERA (multi-scale entanglement renormalization ansatz). Moreover, we study this correspondence from the viewpoint of entanglement entropy and an information metric. The Cramer–Rao bound in quantum estimation theory implies that the quantum fluctuations of the radial coordinate of the AdS are highly suppressed in the large-N limit.