Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime

TL;DR

This paper introduces quantum extremal surfaces as a way to compute holographic entanglement entropy beyond classical approximations, incorporating quantum corrections at all orders in the bulk Planck constant.

Contribution

It proposes a new method using quantum extremal surfaces to calculate holographic entanglement entropy at arbitrary quantum orders, extending previous leading-order results.

Findings

Quantum extremal surfaces extremize the generalized entropy.

At leading order, the proposal agrees with existing formulas.

Beyond leading order, the conjecture diverges from prior results.

Abstract

We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.