We investigate the extension of a holographic construction for the entanglement negativity of two disjoint subsystems in proximity to CF T d s with a conserved charge dual to bulk AdS d+1 geometries. The construction involves a specific algebraic sum of the areas of bulk co-dimension two static minimal surfaces homologous to certain appropriate combinations of the subsystems in question. In this connection we compute the holographic entanglement negativity for two disjoint subsystems in proximity, with long rectangular strip geometries in CF T d s dual to bulk non extremal and extremal RN-AdS d+1 black holes. Our results conform to quantum information theory expectations and also reproduces earlier results for adjacent subsystems in the appropriate limit which constitutes strong consistency checks for our holographic construction.

We obtain the holographic entanglement negativity for bipartite mixed states at a finite temperature in baths described by conformal field theories dual to configurations involving two communicating black holes in braneworld geometries. In this context we analyze the mixed state entanglement structure characterized by the information transfer between the black holes for two separate models. The first model involves communicating black holes in a Karch-Randall braneworld and BCF T 2 s with two boundaries describing common bath systems for the radiation flux. The second model corresponds to a configuration of two dimensional eternal JT black holes in a braneworld geometry involving two Planck branes coupled through shared bath systems described by CF T 2 s. For both the models our results reproduce analogue of the Page curves for the entanglement negativity obtained earlier in the context of random matrix theory and from geometric evaporation in JT black hole configurations.

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT2s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS3/BCFT2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

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