When Symmetry Suppresses Magic
Abstract
Nonstabilizerness is a critical resource for quantum advantage, but evaluating it, especially for mixed states, requires superexponentially many samples in system size, making the problem NP-hard. While symmetries are known to reduce this complexity, it is unclear whether they also restrict the amount of magic. In this work, we provide an explicit example of such a symmetry by proving that the Robustness of Magic (RoM) for N-qubit X-states is at most √3. Leveraging this symmetry constraint, we introduce a computationally efficient method to lower-bound the RoM of arbitrary many-body states, demonstrating its utility on the ground states of a spin-1/2 Hamiltonian with system sizes well beyond the reach of exact evaluation. Furthermore, for Hamiltonians whose equilibrium states are X-states, we analytically derive the critical temperature at which magic emerges. Our work shows why certain symmetries constrain magic while others do not, provides a scalable lower-bounding method, and identifies a nontrivial regime where many-body nonstabilizerness is analytically solvable.
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BibTeX
@misc{junior2026when,
title = {{When Symmetry Suppresses Magic}},
author = {A. de Oliveira Junior and Jake Xuereb and Rafael A. Macêdo and Jonatan Bohr Brask and Rafael Chaves},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38319},
eprint = {2609.38319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38319},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - When Symmetry Suppresses Magic
AU - A. de Oliveira Junior
AU - Jake Xuereb
AU - Rafael A. Macêdo
AU - Jonatan Bohr Brask
AU - Rafael Chaves
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38319
UR - https://arxiv.org/abs/2609.38319
AB - Nonstabilizerness is a critical resource for quantum advantage, but evaluating it, especially for mixed states, requires superexponentially many samples in system size, making the problem NP-hard. While symmetries are known to reduce this complexity, it is unclear whether they also restrict the amount of magic. In this work, we provide an explicit example of such a symmetry by proving that the Robustness of Magic (RoM) for N-qubit X-states is at most √3. Leveraging this symmetry constraint, we introduce a computationally efficient method to lower-bound the RoM of arbitrary many-body states, demonstrating its utility on the ground states of a spin-1/2 Hamiltonian with system sizes well beyond the reach of exact evaluation. Furthermore, for Hamiltonians whose equilibrium states are X-states, we analytically derive the critical temperature at which magic emerges. Our work shows why certain symmetries constrain magic while others do not, provides a scalable lower-bounding method, and identifies a nontrivial regime where many-body nonstabilizerness is analytically solvable.
ER -