Classical Statistical Mechanics Approach to Multipartite Entanglement

Abstract

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

38 pages, 10 figures, published version

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• Planar Maximally Entangled States
• $k$-uniform mixed states
• The classification of multipartite quantum correlation
• State complexity and quantum computation
• Typical Entanglement
• Multi-partite analysis of average-subsystem entropies
• Polarized ensembles of random pure states
• Phase diagram of bipartite entanglement
• A note on the Bloch representation of absolutely maximally entangled states
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• A large-N approximated field theory for multipartite entanglement
• Completely mixed state is a critical point for three-qubit entanglement
• Feynman graphs and the large dimensional limit of multipartite entanglement
• Scalable and fault-tolerant preparation of encoded k-uniform states