Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal

TL;DR

This paper introduces a new minimal entanglement purification criterion based on the entanglement of purification, proposing its holographic dual as a boundary state in the entanglement wedge, and discusses connections to the complexity=action conjecture.

Contribution

It defines a novel minimal purification criterion and links it to holographic duals and complexity proposals in quantum gravity.

Findings

Proposes a new criterion for minimal entanglement purification.

Suggests a holographic dual involving the entanglement wedge boundary.

Discusses relationships between purification, wormhole geometries, and complexity.

Abstract

We define a new criterion for selecting a specific minimal entanglement purification of given mixed states in generic quantum states using the entanglement of purification. We then propose that its holographic dual is the state living on the boundary of the entanglement wedge in the surface-state correspondence. Finally, we make some remarks about the relationship between this and the complexity equals action proposals.