  We study the holographic duality between the reflected entropy and the
entanglement wedge cross section with the first order correction. In the field
theory side, we consider the reflected entropy for $\rho_{AB}^m$, where
$\rho_{AB}$ is the reduced density matrix for two intervals in the ground
state. The reflected entropy in the 2d holographic conformal field theories is
computed perturbatively up to the first order in $m-1$ by using the
semiclassical conformal block. In the gravity side, we compute the entanglement
wedge cross section in the backreacted geometry by cosmic branes with tension
$T_m$ which are anchored at the AdS boundary. Comparing both results we find a
perfect agreement, showing the duality works with the first order correction in
$m-1$.
