  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 $A$, $I^{ss}(E\rangle A)$. 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.

High Energy Physics - Theory;Quantum Physics