  In this article, we investigate the entanglement structure of bipartite mixed
states in (1+1)-dimensional boundary conformal field theories (BCFT$_2$s)
through the odd entanglement entropy (OEE) by employing an appropriate replica
technique. In this regard we compare our results with the bulk entanglement
wedge cross section (EWCS) for AdS$_3$ geometries with an end-of-the-world
brane. We observe consistent extension of the holographic duality between the
difference of the OEE and the entanglement entropy (EE) with the bulk EWCS, in
the framework of AdS$_3$/BCFT$_2$ holography. Furthermore, we also extend our
computations to the holographic moving mirror models where the Hawking
radiation from eternal and evaporating black holes may be simulated depending
on certain mirror profiles, and find consistent extension of the aforementioned
holographic duality.
