标题： 极端Wigner负自旋态的恒星表示 显示英文标题

标题： Stellar representation of extremal Wigner-negative spin states

摘要： 马约拉纳恒星表示法被用于表征在球形相空间上具有最大负Wigner准概率分布的自旋态。 这些具有最大Wigner负值的自旋态通常在其恒星配置中表现出部分但非高度的对称性。 特别是，对于自旋$j > 2$，当可用时，极大星座并不对应于一个正多面体，并且随着维度增加不遵循明显的几何模式。 此外，它们通常不同于最大化其他非经典度量（如反相干性或几何纠缠）的自旋态。 随机态（$j \leq 6$）平均显示相对较高的负值，但在希尔伯特空间中，极值态和具有相似负值的态在统计上是稀有的。 我们还证明了任意维度的所有自旋相干态都具有非零的Wigner负值。 这提供了证据表明所有纯自旋态也具有非零的Wigner负值。 这些结果可以应用于表现出置换不变性的量子比特集合。 显示英文摘要

摘要： The Majorana stellar representation is used to characterize spin states that have a maximally negative Wigner quasiprobability distribution on a spherical phase space. These maximally Wigner-negative spin states generally exhibit a partial but not high degree of symmetry within their star configurations. In particular, for spin $j > 2$, maximal constellations do not correspond to a Platonic solid when available and do not follow an obvious geometric pattern as dimension increases. In addition, they are generally different from spin states that maximize other measures of nonclassicality such as anticoherence or geometric entanglement. Random states ($j \leq 6$) display on average a relatively high amount of negativity, but the extremal states and those with similar negativity are statistically rare in Hilbert space. We also prove that all spin coherent states of arbitrary dimension have non-zero Wigner negativity. This offers evidence that all pure spin states also have non-zero Wigner negativity. The results can be applied to qubit ensembles exhibiting permutation invariance.