  We propose the information-theoretic quantity of geometric quantum discord
(GQD) as an indicator of the factorization properties of a given quantum
system. In particular, we show how non-vanishing discord implies that the
corresponding partition function does not factorize, both for generic pure
states and the thermofield double state as a state with a known geometric dual
in light of the AdS/CFT correspondence. Via this analysis, we give a novel
interpretation to the thermomixed double state as the best purely classical
approximation of the Einstein-Rosen bridge. We connect the non-vanishing of GQD
with the existence of wormhole microstates.
