Asymptotic Entanglement Hiding under Stabilizer Restrictions

Jicun Li; Wei Xie; Jun Wu; Honglin Chen; Xiang-Yang Li

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arXiv · 2608.18440

Asymptotic Entanglement Hiding under Stabilizer Restrictions

Jicun Li·Wei Xie·Jun Wu·Honglin Chen·Xiang-Yang Li

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Abstract

Entanglement is central to quantum information processing, while stabilizer operations underpin fault-tolerant quantum computation. We ask how much entanglement remains visible or distillable under stabilizer restrictions. We quantify stabilizer-visible entanglement by restricting the measured relative entropy of entanglement to stabilizer measurements, thereby obtaining converse bounds on entanglement distillation under stabilizer operations. We demonstrate magic-free asymptotic entanglement hiding: we construct explicit convex mixtures of pure stabilizer states on $N$ qutrits per party whose unrestricted visible entanglement and LOCC-distillable entanglement both grow as $\Omega(N/\log N)$, while their stabilizer-visible and stabilizer-distillable entanglement vanish as $N\to\infty$. Thus, an unbounded amount of LOCC-distillable entanglement carried by stabilizer states can become asymptotically invisible and undistillable under stabilizer restrictions. We further prove that stabilizer-visible entanglement is $O(1)$ with high probability for Haar-random pure states despite extensive unrestricted visibility, and vanishes uniformly over entangled Werner states as the local dimension grows through odd primes. These results reveal a fundamental separation between entanglement and magic as resources, exposing intrinsic limits on entanglement extraction using stabilizer operations.

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Jicun Li, Wei Xie, Jun Wu, Honglin Chen, Xiang-Yang Li. 2026-08-19. Asymptotic Entanglement Hiding under Stabilizer Restrictions. https://arxiv.org/abs/2608.18440

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