Holographic Complexity

Abstract

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 model. We also explore a possible relation between the defined quantity and fidelity appearing in quantum information literature.

revtex, 6 pages, V2: Typos corrected, Comments added, V3: Typos corrected

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• Generalized holographic complexity of rotating black holes
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• Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States
• Weighting gates in circuit complexity and holography
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• Information theoretic measures for Lifshitz system
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