Multipartite entanglement of random states of qubits

Entanglement is a fundamental feature of quantum mechanics and a central resource in quantum information, enabling relevant applications such as quantum teleportation [1–3], quantum computation [4], quantum communication [5] and quantum cryptography [6–9]. While the bipartite entanglement of pure states is unambiguously quantified in terms of the entropy of either single-party reduced state [10–12], the quantification of multipartite entanglement remains more intricate and less unified [13–15]. This has led to multiple approaches being developed, each focusing on different aspects of the problem, for instance the invariance under permutation of the parties [16, 17], the scalability of the measure with the system size [18], the structural analogy with the bipartite von Neumann entropy [13] or the mutual exclusivity of single-partite and bipartite properties of subsystems [19]. These different characterizations of multipartite entanglement often yield distinct and, in some cases, incompatible classifications. Various studies have shown that multipartite entanglement exhibits frustration, i.e., the impossibility of simultaneously maximizing entanglement across all bipartitions [20–24], making statistical methods from complex systems particularly suitable for its characterization. In this context, analyzing the statistical distribution of entanglement measures, such as the purity over all balanced bipartitions and related quantities like the average linear entropy [13, 22, 25],…