We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in (1 + 1)-dimensional conformal field theories in the AdS 3 /CF T 2 framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the CF T 1+1 vacuum dual to bulk the pure AdS 3 geometry and the finite temperature mixed state dual to a Euclidean BTZ black hole respectively. The holographic entanglement negativity characterizes the distillable entanglement and reduces to a specific sum of holographic mutual informations. We briefly allude to a possible higher dimensional generalization of our conjecture in a generic AdS d+1 /CF T d scenario.

We obtain the entanglement negativity for various bipartite zero and finite temperature pure and mixed state configurations in a class of (1 + 1)-dimensional Galilean conformal field theories. In this context we establish a construction for computing the entanglement negativity for such bipartite states involving a suitable replica technique. Our construction exactly reproduces certain universal features observed for entanglement negativity of corresponding states in relativistic (1 + 1)-dimensional conformal field theories. *

No abstract

We investigate the application of our recent holographic entanglement negativity conjecture for higher dimensional conformal field theories to specific examples which serve as crucial consistency checks. In this context we compute the holographic entanglement negativity for bipartite pure and finite temperature mixed state configurations in d-dimensional conformal field theories dual to bulk pure Ad S d+1 geometry and Ad S d+1 -Schwarzschild black holes respectively. It is observed that the holographic entanglement negativity characterizes the distillable entanglement for the finite temperature mixed states through the elimination of the thermal contributions. Significantly our examples correctly reproduce universal features of the entanglement negativity for corresponding two dimensional conformal field theories, in higher dimensions.

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in (1 + 1) dimensional conformal field theories (C FT 1+1) dual to bulk non static Ad S 3 geometries. Application of our proposal to such mixed states in a C FT 1+1 dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a C FT 1+1 dual to a bulk Vaidya-Ad S 3 geometry in the context of their thermalization involving bulk black hole formation.