Holographic complexity

For a field theory with a gravitational dual, following Susskind's proposal we define holographic complexity for a subsystem. The holographic complexity is proportional to the volume of a codimension one time slice in the bulk geometry enclosed by the extremal codimension two hypersurface appearing in the computation of the holographic entanglement entropy. The proportionally constant, up to a numerical order of 1 factor is $GR$ where G is the Newton constant and R is the curvature of the space-time. We study this quantity in certain holographic models. We also explore a possible relation between the defined quantity and fidelity appearing in quantum information literature.