Holographic Complexity

TL;DR

This paper proposes a holographic measure of complexity for subsystems in theories with gravitational duals, relating it to bulk volume and exploring its connection to quantum fidelity.

Contribution

It introduces a new holographic complexity measure based on bulk volume and investigates its properties and potential relation to quantum information fidelity.

Findings

Holographic complexity is proportional to bulk volume enclosed by extremal surfaces.

The measure is studied in specific holographic models.

A possible link between holographic complexity and quantum fidelity is explored.

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.