Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes

TL;DR

This paper introduces a semiclassical flow in holographic spacetimes that coarse-grains states by disentangling short-distance degrees of freedom, connecting to quantum extremal surfaces and quantum error correction.

Contribution

It generalizes classical holographic coarse-graining to include quantum corrections using generalized entropy, revealing a flow towards quantum extremal surfaces.

Findings

Flow approaches quantum extremal surfaces

Inclusion of quantum corrections via generalized entropy

Connection to quantum error correction in holography

Abstract

Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states. The coarse-graining procedure involves identifying degrees of freedom entangled at short distances and disentangling them. This is manifested in the bulk by a flow equation that generates a codimension-1 object, which we refer to as the holographic slice. We generalize the earlier classical construction to include bulk quantum corrections, which naturally involves the generalized entropy as a measure of the number of relevant boundary degrees of freedom. The semiclassical coarse-graining results in a flow that approaches quantum extremal surfaces such as entanglement islands that have appeared in discussions of the black hole information paradox. We also discuss the relation of the present picture to the view that the holographic dictionary works as quantum error correction.