Hadamard states exhibit higher average multipartite entanglement than Haar-typical states via purity of balanced bipartitions, with hypergraph states (real alternating-sign coefficients) being especially promising for maximal entanglement due to simplicity and sampling likelihood.
Mezzadri, How to generate random matrices from the classical compact groups, Notices of the American Math- ematical Society54, 592 (2007)
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Multipartite entanglement of random states of qubits
Hadamard states exhibit higher average multipartite entanglement than Haar-typical states via purity of balanced bipartitions, with hypergraph states (real alternating-sign coefficients) being especially promising for maximal entanglement due to simplicity and sampling likelihood.