AI 中文总结
研究非可分 Werner 态在\(S_{1}\times S_{2}\)设置下的贝尔局域性，通过分析找到新条件，证明了特定维度态的局域性，其结果对贝尔非局域性理论及相关量子应用有重要意义。
AI 中文摘要
在许多量子应用中，了解贝尔非局域两量子比特态在两个地点具有给定数量\(S_{1},S_{2}\geq1\)的广义量子测量的相关场景下是否展现非局域性很重要。本文通过分析找到了一个新的一般条件，对于维度\(d\leq\min\{S_{1},S_{2}\}\)的非可分 Werner 态，在任意谱类型（离散或连续）的每个\(S_{1}\times S_{2}\)设置相关场景下满足所有贝尔不等式，即\(S_{1}\times S_{2}\)设置贝尔局域。对于多种\(S_{1},S_{2}\geq1\)值，该条件超越了 Werner 和 Barrett 对非可分 Werner 态的局域性条件。还通过半编程以算子形式明确证明了 Terhal 等人的优化结果，即维度\(d>\min\{S_{1},S_{2}\}\)的每个非可分 Werner 态是\(S_{1}\times S_{2}\)设置贝尔局域。本文新结果对贝尔非局域性理论和基于贝尔非局域性的量子应用都很重要。
英文摘要
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers $S_{1},S_{2}\geq1$ of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension $d\leq\min\{S_{1},S_{2}\}$ to satisfy all Bell inequalities under every $S_{1}\times S_{2}$-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous $-$ that is, to be $S_{1}\times S_{2}$-setting Bell local, for short. For a variety of $S_{1},S_{2}\geq1$ values, this new general locality condition is beyond Werner's and Barrett's locality conditions for a nonseparable Werner state. We also prove explicitly in the operator terms the optimization result by Terhal et. el. [Phys. Rev. Lett. \textbf{90,} 157903 (2003)] via semi-programming that every nonseparable Werner state with a dimension $d>\min\{S_{1},S_{2}\}$ is $S_{1}\times S_{2}$ -setting Bell local. The new results of the present article are important both for Bell nonlocality theory and for quantum applications based on Bell nonlocality.
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