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Tripartite information of highly entangled states
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abstract
Holographic systems require monogamous mutual information for validity of semiclassical geometry. This is encoded by the sign of the tripartite information ($I3$). We investigate the behaviour of $I3$ for all partitionings of systems in states which are highly entangled in a multipartite or bipartite sense. In the case of multipartite entanglement we propose an algorithmic construction that we conjecture can be used to build local maxima of $I3$ for any partitioning. In case of bipartite entanglement we classify the possible values of $I3$ for perfect states and investigate, in some examples, the effect on its sign definiteness due to deformations of the states. Finally we comment on the proposal of using $I3$ as a parameter of scrambling, arguing that in general its average over qubits permutations could be a more sensible measure.
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Tripartite entanglement of qudits
The authors prove a decomposition theorem for algebraic entanglement invariants of tripartite qudit states and use it to enumerate all entanglement classes for three qutrits.
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