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This research introduces a linear Stabilizer Entropy measure that effectively quantifies non-stabilizerness in mixed quantum states where exact calculation is provably impossible. The proposed metric maintains monotonicity with overwhelming probability under specific Clifford channels, offering a practical and theoretically sound alternative for resource estimation in many-body systems.

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Stabilizer entropy is trustworthy for mixed states

arXiv28 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2606.29443v3 Announce Type: replace Abstract: Quantifying non-stabilizerness in mixed states is provably intractable, as any strict monotone requires superexponential time. We propose a linear Stabilizer Entropy that acts as a proper non-stabilizerness monotone with overwhelming probability when restricted to non-adaptive Clifford channels acting on flat mixed stabilizer states. Analytical and numerical results for Haar-random states, Clifford orbits, and random matrix product states show that monotonicity violation probabilities decay as $\exp-\eta N$. We also prove the validity of Stabilizer Entropy in specific many-body systems undergoing partial measurements, where the amount of resource never increases for each measurement outcome as well as when averaged over outcome probabilities. Given the hardness of strict alternatives, Stabilizer Entropy emerges as a practical and theoretically justified resource measure.

Abstract:Quantifying non-stabilizerness in mixed states is provably intractable, as any strict monotone requires superexponential time. We propose a linear Stabilizer Entropy that acts as a proper non-stabilizerness monotone with overwhelming probability when restricted to non-adaptive Clifford channels acting on flat mixed stabilizer states. Analytical and numerical results for Haar-random states, Clifford orbits, and random matrix product states show that monotonicity violation probabilities decay as $\exp-\eta N$. We also prove the validity of Stabilizer Entropy in specific many-body systems undergoing partial measurements, where the amount of resource never increases for each measurement outcome as well as when averaged over outcome probabilities. Given the hardness of strict alternatives, Stabilizer Entropy emerges as a practical and theoretically justified resource measure.

arXiv:2606.29443 [quant-ph]

(or arXiv:2606.29443v3 [quant-ph] for this version)

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