Spectral geometry of nonlocal stabilizer entropy

• URL: http://arxiv.org/abs/2609.13106v2
• Date: Mon, 14 Sep 2026 17:48:32 GMT
• Title: Spectral geometry of nonlocal stabilizer entropy
• Abstract summary: We prove a conjecture for two families of states at every system size and bipartition.<n>For arbitrary bipartite pure states, we show that the CB value exceeds the nonlocal SRE by at most $4$.<n>We apply these results to the transverse-field Ising chain, where we tightly bound the nonlocal SRE in the gapped phases and identify its double-logarithmic growth at criticality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic, or nonstabilizerness, is the resource that promotes stabilizer operations to universal quantum computation. For bipartite pure states, its component intrinsic to the correlations between the subsystems, the nonlocal magic, is obtained by minimizing a magic measure over local unitaries. For the stabilizer Rényi entropy (SRE), the minimum is conjectured to be attained by the computational-basis (CB) representative, the state obtained by assigning the Schmidt coefficients in decreasing order to matching computational-basis labels. We prove this conjecture for two families of states at every system size and bipartition: states with dyadic-staircase Schmidt spectra and states of Schmidt rank at most six. For arbitrary bipartite pure states, we show that the CB value exceeds the nonlocal SRE by at most $4$, fixing the leading term of any divergent scaling of nonlocal SRE. We further show that the nonlocal SRE grows at most logarithmically with the entanglement entropy. Consequently, one-dimensional area-law states have bounded nonlocal SRE, while critical states with logarithmic entanglement entropy permit at most doubly logarithmic growth with system size. We apply these results to the transverse-field Ising chain, where we tightly bound the nonlocal SRE in the gapped phases and identify its double-logarithmic growth at criticality.

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