Conditional and Multipartite Entanglements of Purification and Holography

TL;DR

This paper extends the concept of entanglement of purification to conditional and multipartite forms, deriving new constraints and inequalities that support the holographic duality conjecture and offer consistency checks for bulk geometries.

Contribution

It introduces generalized conditional and multipartite entanglement of purification concepts, derives new constraints, and analyzes their holographic duals, advancing understanding of entanglement in holography.

Findings

New constraints on conditional entanglement of purification

Multipartite objects are not holographic duals of each other

Inequalities specific to bulk objects for consistency checks

Abstract

In this work we generalize the entanglement of purification and its conjectured holographic dual to conditional and multipartite versions of the same, where the optimization defining the entanglement of purification is now optimized in either a constrained way or over multiple parties. We separately derive new constraints on both the conditional entanglement of purification and its conjectured holographic dual object that match, further reinforcing the likelihood of this conjecture. We also show that the multipartite objects we define, despite obeying several of the same inequalities, are not holographic duals of each other. Further, we find inequalities that are true only for the bulk objects, and thus could provide additional consistency checks for states dual to (semi)-classical bulk geometries.