Canonical purification and the quantum extremal shock

A bstract We study the canonical purification of pure, bi-partite states (with respect to one parties) obtained by turning on sources in Euclidean path integral. In holographic conformal field theories, Lorentzian bulk dual consists corresponding entanglement wedge glued its CRT image at quantum extremal surface. However, mismatch classical expansions QES due corrections needs be supported a shock matter stress tensor order for satisfy Einstein’s equations. Working perturbatively first double-trace around thermofield double state, we demonstrate that state canonically purified boundary CFT precisely has this tensor. interpret our results as emergence gravitational physics from structure context where are important.