An easily computable measure of Gaussian quantum imaginarity

• URL: http://arxiv.org/abs/2504.08132v1
• Date: Thu, 10 Apr 2025 21:21:48 GMT
• Title: An easily computable measure of Gaussian quantum imaginarity
• Authors: Ting Zhang, Jinchuan Hou, Xiaofei Qi,
• Abstract summary: We propose a computable Gaussian imaginarity measure $mathcal IG_n$ for $n$-mode Gaussian systems.<n>A comparative analysis of $mathcalIG_n$ with existing two Gaussian imaginarity measures indicates that $mathcalIG_n$ can be used to detect imaginarity in any $n$-mode Gaussian states more efficiently.
• Score: 4.3414527320532725
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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