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

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.

10 pages, 1 figure. Citations added, and minor clarifications in the body

References in corpus (3)

• Surface/State Correspondence as a Generalized Holography
• Conditional and Multipartite Entanglements of Purification and Holography
• Pulling the Boundary into the Bulk

Cited by in corpus (4)

• Holographic Entanglement of Purification from Conformal Field Theories
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Improved proof-by-contraction method and relative homologous entropy inequalities