An easily computable measure of Gaussian quantum imaginarity
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866913788600516608 |
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| author | Zhang, Ting Hou, Jinchuan Qi, Xiaofei |
| author_facet | Zhang, Ting Hou, Jinchuan Qi, Xiaofei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An easily computable measure of Gaussian quantum imaginarity Zhang, Ting Hou, Jinchuan Qi, Xiaofei Quantum Physics Mathematical Physics 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. |
| title | An easily computable measure of Gaussian quantum imaginarity |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2504.08132 |