论文标题
从随机测量中表征纠缠维度
Characterizing entanglement dimensionality from randomized measurements
论文作者
论文摘要
我们考虑通过在随机方向上测量之间使用相关性来检测纠缠的维度的问题。首先，利用最近得出的协方差矩阵标准用于纠缠维度[S. Liu等人，Arxiv：2208.04909]，我们得出了类似于著名的纠缠标准的不平等，但对于纠缠的不同维度包含不同的范围。该标准在$ su（d）$ bases的局部变化下是不变的，可用于在随机相关的矩中找到区域，从而推广[S. Imai等人，物理。莱特牧师。 126，150501（2021）]纠缠差检测的情况。特别是，我们发现在所有维度的随机相关性的二阶和四阶矩的空间中，分析边界曲线$ d_a = d_a = d_b = d_b = d $ d_b = d $。然后，我们展示了我们的方法在实践中的工作方式，还考虑了有限的相关性统计样本，并且我们还表明，它可以比文献中可用的其他纠缠差异标准比其他纠缠差异标准更能检测到状态，从而提供了一种非常强大且在实际场景中具有更简单的方法。我们通过讨论在多部分方案中实施我们方法的部分开放问题来结束。
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of $su(d)$ bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions $d_a = d_b = d$ of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario.
