Tripartite information of highly entangled states

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.

16 pages. v2: typos fixed, published version

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• Quantum scrambling via accessible tripartite information
• Quantum Thermal Amplifiers with Engineered Dissipation
• An operational definition of quantum information scrambling
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Quantum Information Approaches to Quantum Gravity