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

Abstract

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 Rényi entropy (SRE) in terms of Rényi 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.