Correlation measures and distillable entanglement in $\mathrm{AdS}/\mathrm{CFT}$

Journal Article · Thu Feb 13 00:00:00 EST 2020 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.101.046015· OSTI ID:1599510

Levin, Joshua ; DeWolfe, Oliver; Smith, Graeme

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.

• Research Organization: Univ. of Colorado, Boulder, CO (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0010005; SC0020386
• OSTI ID: 1599510
• Alternate ID(s): OSTI ID: 1762007
• Journal Information: Physical Review D, Journal Name: Physical Review D Vol. 101 Journal Issue: 4; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Gauge-gravity dualities
Quantum correlations in quantum information
Quantum gravity