Quantum Maximin Surfaces

TL;DR

This paper introduces a quantum generalization of maximin surfaces, proves their equivalence to minimal quantum extremal surfaces, and demonstrates that the quantum extremal surface prescription satisfies key entanglement properties, even in complex regimes.

Contribution

It formulates quantum maximin surfaces, proves their equivalence to quantum extremal surfaces, and establishes that the entanglement wedge prescription satisfies entanglement wedge nesting and strong subadditivity.

Findings

Quantum maximin surfaces are equivalent to minimal quantum extremal surfaces.

The entanglement wedge prescription satisfies entanglement wedge nesting.

The prescription also satisfies strong subadditivity, even in complex regimes.

Abstract

We formulate a quantum generalization of maximin surfaces and show that a quantum maximin surface is identical to the minimal quantum extremal surface, introduced in the EW prescription. We discuss various subtleties and complications associated to a maximinimization of the bulk von Neumann entropy due to corners and unboundedness and present arguments that nonetheless a maximinimization of the UV-finite generalized entropy should be well-defined. We give the first general proof that the EW prescription satisfies entanglement wedge nesting and the strong subadditivity inequality. In addition, we apply the quantum maximin technology to prove that recently proposed generalizations of the EW prescription to nonholographic subsystems (including the so-called "quantum extremal islands") also satisfy entanglement wedge nesting and strong subadditivity. Our results hold in the regime where backreaction of bulk quantum fields can be treated perturbatively in $G_{N}\hbar$, but we emphasize that they are valid even when gradients of the bulk entropy are of the same order as variations in the area, a regime recently investigated in new models of black hole evaporation in AdS/CFT.