We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

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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 propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS 3 /BCFT 2 framework. Furthermore, in the time-dependent AdS 3 /BCFT 2 scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.