Correlation measures and distillable entanglement in AdS/CFT

Abstract

Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced $Q$-correlation and $R$-correlation, $E_Q$ and $E_R$. We find that $E_Q$ admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region $A$ and a cross-section of $A$'s entanglement wedge with $B$. We note a strict trade-off between this minimal mutual information and the symmetric side-channel assisted distillable entanglement from the environment $E$ to $A$, $I^{ss}(E⟩A)$. We also show that the $R$-correlation, $E_R$, coincides holographically with the entanglement wedge cross-section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories.

arXiv comment12 pages, 5 figures. v2: typos and minor corrections, references added

References in corpus (26)

• A computable measure of entanglement
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Monogamy of entanglement and other correlations
• "Squashed Entanglement" - An Additive Entanglement Measure
• Holographic Entanglement of Purification
• Holographic Mutual Information is Monogamous
• The entanglement of purification
• Entanglement of purification: from spin chains to holography
• Surface/State Correspondence as a Generalized Holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Bit threads and holographic entanglement
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Geometric Aspects of Holographic Bit Threads
• Entanglement of Purification for Multipartite States and its Holographic Dual
• The quantum capacity with symmetric side channels
• Bit threads and holographic entanglement of purification
• On quantum advantage in dense coding
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Bit threads and holographic entanglement of purification
• Towards a Bit Threads Derivation of Holographic Entanglement of Purification
• The quantum one-time pad in the presence of an eavesdropper
• Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
• Optimized Measures of Bipartite Quantum Correlation
• Public Quantum Communication and Superactivation

Cited by in corpus (13)

• Holographic Pseudo Entropy
• Islands for Reflected Entropy
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Quantum and Classical Correlations Inside the Entanglement Wedge
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Balanced Partial Entanglement and Mixed State Correlations
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Ownerless island and partial entanglement entropy in island phases
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Optimized Correlation Measures in Holography
• Multipartite Optimized Correlation Measures and Holography
• Phase Transitions of Correlations in Black Hole Geometries