The Ryu-Takayanagi proposal was extended to time dependent states by Hubeny-Rangamany-Takayanagi.
Swingle as well as van Raamsdonk argued that the essential building blocks of spacetime geometry should be related to entanglement structure.
This opened up the door of the reconstruction of the bulk geometry from purely quantum considerations. Susskind-Maldacena dictums like ER=EPR are related to this aspect.
Faulkner-Lewkowycz-Maldacena proposed quantum corrections to HEE in 2013.