Odd entanglement entropy in boundary conformal field theories and holographic moving mirrors

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.