Correlation measures and distillable entanglement in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>AdS</mml:mi><mml:mo>/</mml:mo><mml:mi>CFT</mml:mi></mml:mrow></mml:math>
Joshua Levin, Oliver DeWolfe, Graeme Smith
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.