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

We obtain the odd entanglement entropy (OEE) for bipartite mixed states in $(1+1)$-dimensional boundary conformal field theories (BCFT₂s) utilizing an appropriate replica technique. For the generic configuration of two disjoint intervals, the large-c factorization of the twist field correlator leads to several distinct phases depending on the relative sizes and separations of the intervals. The resulting expressions match consistently with the entanglement wedge cross section (EWCS) for the bulk AdS₃ braneworld geometries, thereby extending the proposed holographic duality between the difference of the OEE and the entanglement entropy with the EWCS to BCFT setups. Furthermore, we obtain the OEE for these mixed states in related holographic moving mirror models which simulate Hawking radiation from black holes and verify the above duality in these time-dependent backgrounds. In this context we analyze the time evolution of the OEE and establish the analogues of Page curves for this mixed-state correlation measure.