# Quantum extremal surface (QES) The quantum extremal surface (QES) generalises the [[0007 RT surface|RT-HRT]] formula by including quantum corrections to all orders in $\hbar$. It states that the quantum-corrected entanglement entropy is given by an extremum of the sum of an area term and a bulk entropy term. See refs for details. ## Refs - [[1986#Bombelli, Koul, Lee, Sorkin]] - one of the very earliest proposals for splitting the entropy to be BH + matter field outside - [[2013#Faulkner, Lewkowycz, Maldacena]] - one-loop correction - [[2014#Engelhardt, Wall]] - to all orders - [[2025#Colin-Ellerin, Lin, Penington]] - careful treatment of gravitons ## Properties - thermodynamics of QES - [[PedrazaSveskoSybesmaVisser2021]][](https://arxiv.org/pdf/2107.10358.pdf) - bulk interpretation - [[2022#Wong]] ## Examples - in various spacetimes - [[ManuNarayanPaul2020]] - for photons in AdS - [[2024#Colin-Ellerin, Lin]] ## Related topics - [[0145 Generalised area]] - [[0007 RT surface]] - [[0213 Islands]]