Holographic Entanglement of Purification from Conformal Field Theories

Abstract

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples.

7 pages, Revtex, 5 figures

References in corpus (7)

• A class of quantum many-body states that can be efficiently simulated
• Complexity and Shock Wave Geometries
• Causality & holographic entanglement entropy
• Gravitational action with null boundaries
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Surface/State Correspondence as a Generalized Holography
• Einstein's Equations from Varying Complexity

Cited by in corpus (15)

• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Some Aspects of Entanglement Wedge Cross-Section
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Multipartite Reflected Entropy
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Balanced Partial Entanglement and Mixed State Correlations
• Path-Integral Optimization from Hartle-Hawking Wave Function
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Entanglement wedge cross-section in shock wave geometries
• Multipartite Optimized Correlation Measures and Holography
• Non-Conformal Behavior of Holographic Entanglement Measures
• Holographic Complexity from the Crofton's Formula in Lorentzian AdS${}_3$
• Phase Transitions of Correlations in Black Hole Geometries
• Purification Complexity without Purifications
• A note on the kinematic space associated with a subregion