The holographic entanglement entropy proposals give an explicit geometric encoding of spatially ordered quantum entanglement in continuum quantum field theory. These proposals have been developed in the context of the AdS/CFT correspondence, which posits a quantum duality between gravitational dynamics in anti-de Sitter (AdS) space times and that of a conformal field theory (CFT) in one fewer dimension. The von Neumann entropy of a spatial region of the CFT is given by the area of a particular extremal surface in the dual geometry. This surprising connection between a fundamental quantum mechanical concept and a simple geometric construct has given deep insights into the nature of the holographic map and potentially holds an important clue to unraveling the mysteries of quantum gravity.
