  Recently, the reflected entropy is proposed in holographic approach to
describe the entanglement of a bipartite quantum system in a mixed state, which
is identified as the area of the reflected minimal surface inside the
entanglement wedge. In this paper, we study the reflected entropy in the doubly
holographic setup, which contains the degrees of freedom of quantum matter in
the bulk. In this context, we propose a notion of quantum entanglement wedge
cross-section, which may describe the reflected entropy with higher-order
quantum corrections. We numerically compute the reflected entropy in pure AdS
background and black hole background in four dimensions, respectively. In
general, the reflected entropy contains the contribution from the geometry on
the brane and the contribution from the CFT. We compute their proportion for
different Newton constants and find that their behaviors are in agreement with
the results based on the semi-classical gravity and the correlation of CFT
coupled to the bath CFT.
