AI 中文总结
该研究提出用图论方法解决量子非稳定子性检测难题，明确了两个耦合障碍，证明了符号依赖可舍弃的条件，导出了闭式，利用克利福德协变性扩大了可检测态空间，为魔资源检测提供了可扩展设计原则。
AI 中文摘要
检测非稳定子性需要全量子态层析以及对指数多个稳定子态的优化。有限的泡利测量集有望实现资源高效的魔态认证，但由此产生的约化稳定子多面体通常难以表征。我们将这一困难追溯到两个耦合障碍：由测量的 frustration 图结构所表征的测量同时可测性，以及来自稳定子形式论的符号依赖一致性。我们证明，当不存在主动依赖时，符号依赖可被精确舍弃，而完美的 frustration 图会使该约化多面体变得可高效求解。该可求解 regime 导出了一个以 frustration 图团数为界的闭式，揭示了见证容量与同时可测性之间的权衡关系。克利福德协变性允许旋转后的测量集在不提升容量的情况下扩大可检测态空间。因此，图结构既成为可处理性的证明，也成为可扩展魔资源检测的设计原则。
英文摘要
Detecting nonstabilizerness requires full tomography and an optimization over exponentially many stabilizer states. A limited Pauli measurement set promises resource-efficient magic certification, yet the resulting reduced stabilizer polytope is generally difficult to characterize. We trace this difficulty into two coupled obstructions: the simultaneous measurability of measurements captured by their frustration graph structure, and the consistency of sign dependencies from stabilizer formalism. We show that the sign dependencies can be discarded exactly whenever active dependencies are absent, and that perfect frustration graphs then make this reduced polytope efficiently solvable. This solvable regime derives a closed form bounded by the clique number of the frustration graph, revealing a tradeoff between witness capacity and simultaneous measurability. Clifford covariance allows rotated measurement sets to enlarge the detectable state space without raising the capacity. Graph structure therefore emerges as both a certificate of tractability and a design principle for scalable magic resource detection.
Comments14 pages, 3 figures
