Pearson相关系数用于高维纠缠的验证和量化
Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
摘要：
最近提出了一种使用皮尔逊相关系数（PCC）给出的相关性统计测量来表征纠缠的方案，该方案在量子比特情况下尚未探索。为了将该方案应用于高维态，在最近的一项工作中，通过实验确定PCC并将其解析地与负性相关联来量化空间相关光子量子的经验产生的二分纯态的纠缠，迈出了关键的一步。出于这项工作的动机，我们在这里提出了一个全面的研究，这样的纠缠表征计划的有效性的范围内的二分四重态，通过考虑适当的组合PCC的基础上有限数量的测量。为此，我们研究了由最大纠缠态分别与白噪声和色噪声混合而成的二元态的纠缠的充要证明和量子化问题.此外，通过考虑d=4和5的这些状态类别，讨论了这种基于PCC的方法在更高维度d下的扩展。
英文摘要：
A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of this scheme for the high dimensional states, a key step has been taken in a very recent work by experimentally determining PCC and analytically relating it to Negativity for quantifying entanglement of the empirically produced bipartite pure state of spatially correlated photonic qutrits. Motivated by this work, we present here a comprehensive study of the efficacy of such an entanglement characterizing scheme for a range of bipartite qutrit states by considering suitable combinations of PCCs based on a limited number of measurements. For this purpose, we investigate the issue of necessary and sufficient certification together with quantification of entanglement for the two-qutrit states comprising maximally entangled state mixed with white noise and coloured noise in two different forms respectively. Further, by considering these classes of states for d=4 and 5, extension of this PCC based approach for higher dimensions d is discussed.
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