发表机构
Universidad de Guadalajara（瓜达拉哈拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种优化离散Wigner表示方法，使稳定子态具有精确delta函数表示，并基于此定义非稳定子见证者，为量子比特系统提供几何相空间诊断工具。
AI 中文摘要
量子比特系统中缺乏针对稳定子态的相空间描述这一表面现象并非根本性的，而是源于固定了与状态无关的离散Wigner映射。通过一个简单的优化过程，使相空间表示适应于状态，我们证明了每个量子比特稳定子态对于任何固定的相空间划分都允许存在精确的delta函数离散Wigner表示。这种优化可以直接在测量统计层面实现，通过选择构成划分的互无偏基中的最大概率。这一构造自然导致了一个非稳定子见证者，其定义为Wigner函数在原点的优化值。稳定子态饱和了该见证者对纯态所设定的通用下界，而严格大于该下界的值则证明了非稳定子性。尽管该见证者并非有限大小的资源单调量，但在大量子比特极限下，它变得高度集中，并在随机Clifford变换下实际上保持不变，这表明对于广泛类别的非稳定子态，存在渐近线性增长律。我们的结果恢复了对量子比特稳定子结构的有意义的几何相空间表征，并提供了一种非稳定子性的操作性诊断。
英文摘要
The apparent absence of a stabilizer-specific phase-space description for qubit systems is not fundamental, but arises from fixing a state-independent discrete Wigner map. Allowing the phase-space representation to adapt to the state through a simple optimization procedure, we prove that every qubit stabilizer state admits an exact delta-function discrete Wigner representation for any fixed phase-space partition. This optimization can be implemented directly at the level of measurement statistics by selecting maximal probabilities across mutually unbiased bases forming the partition. This construction naturally leads to a non-stabilizer witness defined by the optimized value of the Wigner function at the origin. Stabilizer states saturate the universal lower bound of this witness for pure states, whereas a value strictly larger than the bound certifies non-stabilizerness. Although the witness is not a finite-size resource monotone, it becomes sharply concentrated and effectively invariant under random Clifford transformations in the large-qubit limit, suggesting an asymptotically linear growth law for broad families of non-stabilizer states. Our results restore a meaningful geometric phase-space characterization of qubit stabilizer structure and provide an operational diagnostic of non-stabilizerness.
