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 s s ( 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.
展开▼
