标题： 一种易于计算的高斯量子虚性度量 显示英文标题

标题： An easily computable measure of Gaussian quantum imaginarity

摘要： 近年来已经开发了量子幻象资源理论框架。在这些框架内，提出了许多有限维系统的幻象度量。然而，对于连续变量（CV）系统中的高斯态的幻象，只有两种已知的高斯幻象度量，在应用于多模态高斯态时表现出禁用的计算复杂性。本文提出了一种可计算的高斯幻象度量$\mathcal I^{G_n}$对于$n$模高斯系统。$\mathcal I^{G_n}$的值可以通过高斯态的位移向量和协方差矩阵简单地表示出来。与现有的两种高斯幻象度量相比，$\mathcal{I}^{G_n}$的比较分析表明，$\mathcal{I}^{G_n}$可以更有效地检测任意$n$模高斯态中的幻象。 作为应用，我们利用${\mathcal I}^{G_2}$研究了两模连续变量系统在高斯马尔可夫噪声环境中$(1+1)$模高斯态的动力学行为。此外，我们证明了${\mathcal I}^{G_n}$可以量化满足多模多体高斯关联度量所有要求的任意$m$多模多体连续变量系统，这揭示了$n$模高斯虚数也可以被视为一种多体多模高斯关联，并且是一种多体高斯量子资源。 显示英文摘要

摘要： The resource-theoretic frameworks for quantum imaginarity have been developed in recent years. Within these frameworks, many imaginarity measures for finite-dimensional systems have been proposed. However, for imaginarity of Gaussian states in continuous-variable (CV) systems, there are only two known Gaussian imaginarity measures, which exhibit prohibitive computational complexity when applied to multi-mode Gaussian states. In this paper, we propose a computable Gaussian imaginarity measure $\mathcal I^{G_n}$ for $n$-mode Gaussian systems. The value of $\mathcal I^{G_n}$ is simply formulated by the displacement vectors and covariance matrices of Gaussian states. A comparative analysis of $\mathcal{I}^{G_n}$ with existing two Gaussian imaginarity measures indicates that $\mathcal{I}^{G_n}$ can be used to detect imaginarity in any $n$-mode Gaussian states more efficiently. As an application, we study the dynamics behaviour of $(1+1)$-mode Gaussian states in Gaussian Markovian noise environments for two-mode CV system by utilizing ${\mathcal I}^{G_2}$. Moreover, we prove that, ${\mathcal I}^{G_n}$ can induce a quantification of any $m$-multipartite multi-mode CV systems which satisfies all requirements for measures of multipartite multi-mode Gaussian correlations, which unveils that, $n$-mode Gaussian imaginarity can also be regarded as a kind of multipatite multi-mode Gaussian correlation and is a multipartite Gaussian quantum resource.