Asymptotic Entanglement Hiding under Stabilizer Restrictions
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 Ω(N/log N), while their stabilizer-visible and stabilizer-distillable entanglement vanish as N→∞. 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.
Related
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BibTeX
@misc{li2026asymptotic,
title = {{Asymptotic Entanglement Hiding under Stabilizer Restrictions}},
author = {Jicun Li and Wei Xie and Jun Wu and Honglin Chen and Xiang-Yang Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18440},
eprint = {2608.18440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18440},
}
RIS
TY - UNPB
TI - Asymptotic Entanglement Hiding under Stabilizer Restrictions
AU - Jicun Li
AU - Wei Xie
AU - Jun Wu
AU - Honglin Chen
AU - Xiang-Yang Li
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2608.18440
UR - https://arxiv.org/abs/2608.18440
AB - 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 Ω(N/log N), while their stabilizer-visible and stabilizer-distillable entanglement vanish as N→∞. 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.
ER -