Nonlocal nonstabilizerness for slightly entangled quantum many-body states

• URL: http://arxiv.org/abs/2607.10714v1
• Date: Sun, 12 Jul 2026 11:14:43 GMT
• Title: Nonlocal nonstabilizerness for slightly entangled quantum many-body states
• Abstract summary: We propose a Schmidt-reference-state framework that replaces this optimization by a direct construction from the sorted spectrum.<n>We conjecture that the nonlocal stabilizer Rényi entropy (SRE) is given by the SRE corresponding reference state.<n>Our results establish entanglement spectra as a powerful window into irreducible nonstabilizer structures in the entanglement spectrum.
• Score: 3.6661773891142744
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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 Rényi 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.

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