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 poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer α≥2. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer α≥2. 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.
Related
- Antiflatness and nonlocal nonstabilizerness in two-particle scattering processes
- Pauli spectrum and nonstabilizerness of random fermionic Gaussian states
- Universal entanglement embezzlement and divergent nonlocal magic from generic local chaotic quantum evolution
- A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness
- Certifying Nonlocal Spin Quantum Entanglement from Local Tunneling Spectra
BibTeX
@misc{liu2026entanglement,
title = {{Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum}},
author = {Lei-Yi-Nan Liu and Jian Cui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01993},
eprint = {2609.01993},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01993},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum
AU - Lei-Yi-Nan Liu
AU - Jian Cui
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.01993
UR - https://arxiv.org/abs/2609.01993
AB - Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer α≥2. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer α≥2. 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.
ER -