  We study the evolution of conditional mutual information in generic open
quantum systems, focusing on one-dimensional random circuits with interspersed
local noise. Unlike in noiseless circuits, where conditional mutual information
spreads linearly while being bounded by the lightcone, we find that noisy
random circuits with an error rate $p$ exhibit superlinear propagation of
conditional mutual information, which diverges far beyond the lightcone at a
critical circuit depth $t_c \propto p^{-1}$. We demonstrate that the underlying
mechanism for such rapid spreading is the combined effect of local noise and a
scrambling unitary, which selectively removes short-range correlations while
preserving long-range correlations. To analytically capture the dynamics of
conditional mutual information in noisy random circuits, we introduce a
coarse-graining method, and we validate our theoretical results through
numerical simulations. Furthermore, we identify a universal scaling law
governing the spreading of conditional mutual information.
