  Causal shadows are bulk space-time regions between the entanglement wedges
and the causal wedges, their existence encodes deep aspects of the entanglement
wedge reconstruction in the context of subregion duality in AdS/CFT. In this
paper, we study the perturbation theory of the causal shadows and their
relation to the properties of the associated modular flows. We first revisit
the cases of degenerate causal shadows based on known examples, and discuss the
origin for their degeneracy via the local nature of the modular flow. We then
focus on the perturbative case in which the CFT subregion consists of two
spheres separated by a large distance $L\gg R_{1,2}$. The RT surfaces still
agree with the causal horizons, giving a degenerate causal shadow classically.
We compute the corrections to the quantum extremal surfaces (Q.E.S) from the
bulk mutual information, which then give rise to a non-degenerate causal shadow
at order $G_N$. We end by discussing the causal shadow perturbation theory more
generally, in particular we explore the possibility of extracting the
positivity conditions characterizing perturbative causal shadows in the
boundary CFTs.
