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Description
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 co-dimension one time slice in the bulk geometry enclosed by the extremal co-dimension two hyper-surface appearing in the computation of the holographic entanglement entropy. The proportionally constant, up to a numerical order of one factor is $G R$ 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.
