Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
Subregion Action and Complexity
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abstract
We evaluate finite part of the on-shell action for black brane solutions of Einstein gravity on different subregions of spacetime enclosed by null boundaries. These subregions include the intersection of WDW patch with past/future interior and left/right exterior for a two sided black brane. Identifying the on-shell action on the exterior regions with subregion complexity one finds that it obeys subadditivity condition. This gives an insight to define a new quantity named mutual complexity. We will also consider certain subregion that is a part of spacetime which could be causally connected to an operator localized behind/outside the horizon. Taking into account all terms needed to have a diffeomorphism invariant action with a well-defined variational principle, one observes that the main contribution that results to a nontrivial behavior of the on-shell action comes from joint points where two lightlike boundaries (including horizon) intersect. A spacelike boundary gives rise to a linear time growth, while we have a classical contribution due to a timelike boundary that is given by the free energy.
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UNVERDICTED 2representative citing papers
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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Holographic entanglement entropy and complexity for the cosmological braneworld model
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.