Total versus quantum correlations in a two-mode Gaussian state,Communications in Theoretical Physics

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Total versus quantum correlations in a two-mode Gaussian state
Communications in Theoretical Physics ( IF 2.4 ) Pub Date : 2021-03-25 , DOI: 10.1088/1572-9494/abeb60
Jamal El Qars _{1,

2,

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Affiliation

In Li and Luo (2007 Phys. Rev. A 76 032327), the inequality $(1/2){ \mathcal T }\geqslant { \mathcal Q }$ was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total ${ \mathcal T }$ and quantum ${ \mathcal Q }$ correlations in bipartite quantum states. Besides, Hayden et al (2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state, quantifying ${ \mathcal T }$ and ${ \mathcal Q }$ respectively by the quantum mutual information ${{ \mathcal I }}^{G}$ and the entanglement of formation (EoF) ${{ \mathcal E }}_{F}^{G}$ , we verify that ${{ \mathcal E }}_{F,R}^{G}$ is always less than $(1/2){{ \mathcal I }}_{R}^{G}$ when ${{ \mathcal I }}^{G}$ and ${{ \mathcal E }}_{F}^{G}$ are defined via the Rnyi-2 entropy. While via the von Neumann entropy, ${{ \mathcal E }}_{F,V}^{G}$ may even dominate ${{ \mathcal I }}_{V}^{G}$ itself, which partly consolidates the Hayden conjecture, and partly, provides strong evidence hinting that the origin of this counterintuitive behavior should intrinsically be related to the von Neumann entropy by which the EoF ${{ \mathcal E }}_{F,V}^{G}$ is defined, rather than related to the conceptual definition of the EoF ${{ \mathcal E }}_{F}$ . The obtained results show that—in the special case of mixed two-mode Gaussian states—quantum entanglement can be faithfully quantified by the Gaussian Rnyi-2 EoF ${{ \mathcal E }}_{F,R}^{G}$ .

中文翻译：

双模高斯态中的总相关性与量子相关性

在 Li 和 Luo (2007 Phys. Rev. A 76 032327) 中，不等式 $(1/2){ \mathcal T }\geqslant { \mathcal Q }$ 被确定为量子与经典相关的一致性理论的基本假设，用于二分量子态中的总相关 ${ \mathcal T }$ 和量子 ${ \mathcal Q }$ 相关的任意度量。此外，Hayden等人(2006 Commun. Math. Phys. 265 95) 推测，在具有无限维希尔伯特空间的系统内的某些条件下，量子相关性可能不仅占总相关性的一半，而且占总相关性本身。这里，在双模高斯态中，分别由量子互信息量化 ${ \mathcal T }$ 和 ${ \mathcal Q }$ ${{ \mathcal I }}^{G}$ 和形成纠缠 (EoF) ${{ \mathcal E }}_{F}^{G}$ ，我们验证它 ${{ \mathcal E }}_{F,R}^{G}$ 总是小于 $(1/2){{ \mathcal I }}_{R}^{G}$ when ${{ \mathcal I }}^{G}$ 并且 ${{ \mathcal E }}_{F}^{G}$ 通过 Rnyi-2 熵定义。而通过冯诺依曼熵， ${{ \mathcal E }}_{F,V}^{G}$ 甚至可能支配 ${{ \mathcal I }}_{V}^{G}$ 自己，这部分巩固了海登猜想，部分提供了强有力的证据，暗示这种违反直觉行为的起源应该与定义EoF 的冯诺依曼熵有内在相关 ${{ \mathcal E }}_{F,V}^{G}$ ，而不是与 EoF 的概念定义相关 ${{ \mathcal E }}_{F}$ 。获得的结果表明，在混合双模高斯态的特殊情况下，可以通过高斯 Rnyi-2 EoF 忠实地量化量子纠缠 ${{ \mathcal E }}_{F,R}^{G}$ 。

更新日期：2021-03-25

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