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We argue that the holographic formula relating entanglement entropy and thearea of a minimal surface is the key to define the area of surfaces in the(emergent) spacetime from the dual theory on the boundary. So we promote theentropy/area relation to operators to define the "area" observable in aholographic formulation of quantum gravity, then we find a suitable geometricrepresentation for the states, and show that the Ryu-Takayanagi proposal isrecovered in the approximation of semi-classical gravity. Finally, we discussthis picture in the example of a AdS-Black hole.

Area Operators in Holographic Quantum Gravity