Author

Jian Cui

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Preprint Sep 2026

Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum

Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains only partially understood. Here we develop a unified spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive universal upper and lower bounds on the nonlocal stabilizer R\'enyi entropy (SRE) in terms of R\'enyi entanglement entropy and spectral non-uniformity. We apply these bounds to exponentially and algebraically decaying spectra, revealing distinct relations between entanglement and nonlocal nonstabilizerness. For the marginal algebraic spectrum and the Calabrese--Lefevre spectrum, we further introduce a dyadic-shell sandwich construction that bounds the ordered entanglement spectrum by upper and lower shell-flat spectra and determines the asymptotic nonlocal SRE scaling. At one-dimensional conformal critical points, this yields a universal hierarchy of double-logarithmic scaling laws. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.

Lei-Yi-Nan Liu, Jian Cui · 1 citation

Preprint Jul 2026

Nonlocal nonstabilizerness for slightly entangled quantum many-body states

Nonlocal nonstabilizerness quantifies the irreducible magic resource encoded in bipartite entanglement, but its evaluation is generally hindered by a highly nonconvex optimization over local unitary transformations. Here we propose a Schmidt-reference-state framework that replaces this optimization by a direct construction from the sorted Schmidt spectrum. We conjecture that the nonlocal stabilizer R\'enyi entropy (SRE) is given by the SRE of the corresponding reference state, and support this conjecture through analytical and numerical evidences. Our framework makes nonlocal nonstabilizerness efficiently accessible for weakly entangled many-body states whenever the entanglement spectrum is available. Applying it to Haar-random states, critical spin chains, and PXP dynamics, we show that nonlocal SRE captures nonstabilizer structures in the entanglement spectrum that are invisible to conventional entanglement measures. Our results establish entanglement spectra as a powerful window into irreducible nonstabilizer correlations, opening a broadly applicable route to studying nonlocal magic resources of quantum many-body systems in and out of equilibrium.

Lei-Yi-Nan Liu, Jian Cui · 4 citations · ⚡1