Uncomplexity and Black Hole Geometry

TL;DR

This paper defines uncomplexity for mixed states, links it to black hole geometry and subregion duality, and shows how accessible spacetime regions relate to computational power in holographic systems.

Contribution

It introduces a new definition of uncomplexity for mixed states and connects it to black hole interior geometry and entanglement wedges.

Findings

Uncomplexity corresponds to accessible interior spacetime inside the entanglement wedge.

Different operations by Bob relate to growth of specific spacetime regions.

The definition resolves puzzles about uncomplexity in thermofield double states.

Abstract

We give a definition of uncomplexity of a mixed state without invoking any particular definitions of mixed state complexity, and argue that it gives the amount of computational power Bob has when he only has access to part of a system. We find geometric meanings of our definition in various black hole examples, and make a connection with subregion duality. We show that Bob's uncomplexity is the portion of his accessible interior spacetime inside his entanglement wedge. This solves a puzzle we encountered about the uncomplexity of thermofield double state. In this process, we identify different kinds of operations Bob can do as being responsible for the growth of different parts of spacetime.