  Recent studies show that a maximally entangled Schwinger pair creates a
nontraversable Einstein-Rosen~(ER) bridge (wormhole) in the gravitational
theory, which bridges causally not connected parts of the AdS spacetime~[PRL
111, 211603 and 211602]. Same authors raise the possibility of a general
correspondence between a weaker entanglement and curvature. Here, we provide
some clues for such a generalized relation. First, we show that (i)
entanglement and (ii) violation of Kramers-Kronig~(KK) relations appear at the
same critical parameters for a standard two-mode (squeezing) entanglement
interaction. We also include the dampings. Second, we bring a study into
attention: Presence of a spacetime-curvature in vacuum polarization,
electron-positron Schwinger pairs, makes QED also violate the KK relations
without violating the causality. Then, we discuss that these findings are
possible to provide new clues for a generalized relation between entanglement
and spacetime-curvature. Such an interpretation may also save violation of KK
relations from implying the violation of the causality.
