the concept of a quantum extremal surface (QES) is a relatively recent development in theoretical physics, specifically in the study of quantum gravity and the AdS/CFT correspondence. It is an area of active research and there is ongoing investigation into its properties and implications.
The idea of the QES originates from the Ryu-Takayanagi (RT) formula, which relates the entanglement entropy of a certain region in a quantum field theory to the area of a corresponding surface in the gravitational dual theory. The RT formula was later generalized by the Hubeny-Rangamani-Takayanagi (HRT) formula, which incorporates quantum corrections and allows for the possibility of QESs.
While the concept of QESs has shown promise in addressing deep questions about the holographic nature of gravity, such as the emergence of spacetime from quantum entanglement, our understanding of QESs is still developing. The exact properties and behaviors of QESs in various contexts, such as black hole physics and quantum information theory, are actively being explored by physicists.
It's worth noting that the reliability of our understanding of QESs will continue to evolve as new research, experiments, and theoretical developments emerge. As of now, the concept of QESs is a valuable tool for investigating the interplay between gravity and quantum information, but its precise implications and limitations are still the subject of ongoing research and debate.