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• Date of publication Oct 22, 2026

  Multipartite entanglement of random states of qubits

  by Giorgia Trotta , Paolo Scarafile , Paolo Facchi , Giuseppe Magnifico , Angelo Mariano , Giorgio Parisi , Saverio Pascazio , Karol Życzkowski

  We investigate multipartite entanglement via the statistical properties of pure quantum states of $n$-qubits. By analyzing the distribution of purity among balanced bipartitions, we compare Haar-typical states, uniformly distributed on the unit sphere of states, with Hadamard states, being characterized by equal weights in the computational basis. We analyze different ensembles of Hadamard states characterized by their phase distributions. Through analytical and numerical calculations, we show that Hadamard states exhibit, on average, a higher degree of entanglement than Haar-typical states. In addition, we show that a particular class of Hadamard states, characterized by real coefficients with alternating signs, known as hypergraph states, appears especially relevant in the search for maximally multipartite entangled states, both for their structural simplicity and the increased likelihood of sampling highly entangled states. These results identify Hadamard states as a tractable yet promising class for exploring multipartite entanglement structures and advancing the characterization of maximally multipartite entangled quantum states.

  Volume 1 • Issue 1 • 2026

• Date of publication Oct 22, 2026

  An asymmetry lower bound on fermionic non-Gaussianity

  by Filiberto Ares , Michele Mazzoni , Sara Murciano , David Szasz-Schagrin , Pasquale Calabrese , Lorenzo Piroli

  Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

  Volume 1 • Issue 1 • 2026