发表机构
University of Gdańsk; Nicolaus Copernicus University in Toruń（格但斯克大学; 托伦哥白尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了素数维度d≥5下的广义等角测量族，通过解析求解参数区间保证POVM有效性，并利用最大纠缠态导出显式导引不等式，证明量子违背。
AI 中文摘要
我们构造了一个维度相关的广义等角测量族，该族在每一个素数维度d≥5中给出显式的导引见证。该构造由d-1个互无偏测量和一个依赖于参数τ的附加归一化2d-1个厄米算子族组成。后者族的正性是主要的技术问题。我们证明了非中心算子可约化为三维不变块，而剩余的中心算子可在二维子空间中精确求解。两个酉等价的3×3矩阵表示描述了相同的活动谱，但由于Gershgorin界依赖于基，它们产生了不同的Gershgorin包围。结合每个表示中较强的端点，我们得到了一个完全解析的τ的不对称区间，该区间保证了有效的POVM。将该POVM与d-1个MUM结合，得到了一个显式的GEAM。最后，利用最大纠缠实现和先前为广义等角测量导出的局部隐态界，我们在每个素数维度d≥5中获得了显式的导引不等式和保证量子违背的充分判据。
英文摘要
We construct a dimension-dependent family of generalized equiangular measurements that gives explicit steering witnesses in every prime dimension $d\geq5$. The construction consists of $d-1$ mutually unbiased measurements and an additional normalized family of $2d-1$ Hermitian operators depending on a parameter $τ$. Positivity of the latter family is the main technical problem. We show that the noncentral operators reduce to three-dimensional invariant blocks, while the remaining central operator is exactly solvable in a two-dimensional subspace. Two unitarily equivalent $3\times3$ matrix representations describe the same active spectrum, but yield different Gershgorin enclosures because Gershgorin bounds are basis dependent. Combining the stronger endpoint from each representation gives a fully analytic asymmetric interval for $τ$ that guarantees a valid POVM. Combining this POVM with the $d-1$ MUMs yields an explicit GEAM. Finally, using a maximally entangled realization and the local-hidden-state bound previously derived for generalized equiangular measurements, we obtain an explicit steering inequality and a sufficient criterion guaranteeing quantum violation in every prime dimension $d\geq5$.
Comments15 pages
