We consider the quantum information metric of a family of CFTs perturbed by
an exactly marginal operator, which has the dual description of the Euclidean
Janus geometries. We first clarify its two dimensional case dual to the three
dimensional Janus geometry, which recently appeared in arXiv:1507.07555. We
generalize this correspondence to higher dimensions and get a precise agreement
between the both sides. We also show that the mixed-state information metric of
the same family of CFTs has a dual description in the Euclidean version of the
Janus time-dependent black hole geometry.Comment: 12 pages, 1 figure, references added, further typos corrected,
correction include
