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arXiv 1703.03063quant-ph
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双模高斯态的类Einstein-Podolsky-Rosen可分性指标

Einstein-Podolsky-Rosen-like separability indicators for two-mode Gaussian states

Paulina Marian, Tudor A. Marian

备注：
Very close to the published version
发表信息：
J. Phys. A: Math. Theor. 51, 065301 (2018)
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摘要：

利用一对类Einstein-Podolsky-Rosen（EPR）观测量的方差研究了双模高斯态的可分性。我们的出发点受到Duan {\em et al.} [Phys. Rev. Lett. {\bf 84}，2722（2000）]。我们评估的产品和这种方差的总和，以及正则化的总和的归一化形式的最小值。利用Simon的基于密度矩阵的部分转置（PPT）为正的条件的可分性准则[Phys.Rev.Lett. {\bf 84}，2726（2000）]，我们证明了这些极小值本身就是可分性指标。它们似乎量化了最大数量的EPR类相关性，这些相关性可以通过局部操作在双模高斯状态下创建。此外，我们重新考虑了Duan {\em et al.}提出的双模高斯态可分性的类EPR方法。没有提到PPT条件。通过优化它们的类EPR不确定性和的正则化形式，我们导出了任意双模高斯态的可分性指标。我们证明了相应的EPR类可分性条件显然等价于Simon的PPT条件。这两种不同的方法（EPR类和PPT）的一致性提供了一个更好的理解检查可分性问题，其明确的解决方案很久以前发现西蒙涵盖了所有感兴趣的情况。

英文摘要：

We investigate the separability of the two-mode Gaussian states by using the variances of a pair of Einstein-Podolsky-Rosen (EPR)-like observables. Our starting point is inspired by the general necessary condition of separability introduced by Duan {\em et al.} [Phys. Rev. Lett. {\bf 84}, 2722 (2000)]. We evaluate the minima of the normalized forms of both the product and sum of such variances, as well as that of a regularized sum. Making use of Simon's separability criterion, which is based on the condition of positivity of the partial transpose (PPT) of the density matrix [Phys. Rev. Lett. {\bf 84}, 2726 (2000)], we prove that these minima are separability indicators in their own right. They appear to quantify the greatest amount of EPR-like correlations that can be created in a two-mode Gaussian state by means of local operations. Furthermore, we reconsider the EPR-like approach to the separability of two-mode Gaussian states which was developed by Duan {\em et al.} with no reference to the PPT condition. By optimizing the regularized form of their EPR-like uncertainty sum, we derive a separability indicator for any two-mode Gaussian state. We prove that the corresponding EPR-like condition of separability is manifestly equivalent to Simon's PPT one. The consistency of these two distinct approaches (EPR-like and PPT) affords a better understanding of the examined separability problem, whose explicit solution found long ago by Simon covers all situations of interest.

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