It from Qubit Summer School
I will describe a procedure for reconstructing the metric of a general holographic spacetime (up to an overall conformal factor) from distinguished spatial slices - “light-cone cuts” - of the conformal boundary. This reconstruction can be applied to bulk points in causal contact with the boundary. I will also discuss a prescription for obtaining the light-cone cuts from divergences of correlators in the dual field theory.
In this talk I will consider quantum states satisfying an area law for entanglement (e.g. as found in quantum field theory or in condensed matter systems at sufficiently low temperature). I will show that both the boundary state and the entanglement spectrum admit a local description whenever there is no topological order. The proof is based on strong subadditivity of the von Neumann entropy. For topological systems, in turn, I'll show that the topological entanglement entropy quantifies exactly how many extra bits are needed in order to have a local description for the boundary state.