标题： 探索各向异性两量子三态的纠缠、Wigner负性和Bell非定域性 显示英文标题

标题： Exploring entanglement, Wigner negativity and Bell nonlocality for anisotropic two-qutrit states

摘要： 我们引入了一类各向异性的两夸脱态（AITTSs）。这些AITTSs表示为 $\rho _{aiso}=p\left\vert \psi _{\left( \theta,\phi \right) }\right\rangle \left\langle \psi _{\left( \theta ,\phi \right)}\right\vert +(1-p)\frac{1_{9}}{9}$，其中包含 $\left\vert \psi _{\left( \theta,\phi \right) }\right\rangle =\sin \theta \cos \phi \left\vert00\right\rangle +\sin \theta \sin \phi \left\vert 11\right\rangle +\cos\theta \left\vert 22\right\rangle $ 和 $1_{9}=\sum_{j,k=0}^{2}\left\vert jk\right\rangle \left\langle jk\right\vert $。对于给定的 $p\in \lbrack 0,1]$，这些态可以在不同的 ($\theta ,\phi $) 方向上进行调整。 在 ($\theta ,\phi $) = ($\arccos (1/\sqrt{3}),\pi /4$) 的情况下，AITTS 将退化为各向同性的两量子三态 (qutrit) 态$\rho _{iso}$。此外，AITTS 对白噪声 ($\rho _{noise}=1_{9}/9$) 非常敏感。我们详细探讨了 AITTS 的三个性质，包括纠缠性、Wigner 负值性和 Bell 非定域性，采用分析和数值方法。每个性质都由适当的现有标准来见证。我们的部分结果总结如下：(i) 大的纠缠性并不一定意味着高的 Wigner 负值性和强的 Bell 非定域性。(ii) 具有大 Schmidt 数的纯态不一定具有更大的 Wigner 负值性。(iii) 只有当$\left\vert\psi _{\left( \theta ,\phi \right) }\right\rangle $的 Schmidt 数为 3 时，AITTS 在适当的参数范围内才有可能表现出 Bell 非定域性。 显示英文摘要

摘要： We introduce a family of anisotropic two-qutrit states (AITTSs). These AITTSs are expressed as $\rho _{aiso}=p\left\vert \psi _{\left( \theta,\phi \right) }\right\rangle \left\langle \psi _{\left( \theta ,\phi \right)}\right\vert +(1-p)\frac{1_{9}}{9}$ with $\left\vert \psi _{\left( \theta,\phi \right) }\right\rangle =\sin \theta \cos \phi \left\vert00\right\rangle +\sin \theta \sin \phi \left\vert 11\right\rangle +\cos\theta \left\vert 22\right\rangle $ and $1_{9}=\sum_{j,k=0}^{2}\left\vert jk\right\rangle \left\langle jk\right\vert $. For a given $p\in \lbrack 0,1]$, these states are adjustable in different ($\theta ,\phi $) directions. In the case of ($\theta ,\phi $) = ($\arccos (1/\sqrt{3}),\pi /4$), the AITTS will reduce to the isotropic two-qutrit state $\rho _{iso}$. In addition, the AITTSs are severely affected by the white noise ($\rho _{noise}=1_{9}/9$). Three properties of the AITTSs, including entanglement, Wigner negativity and Bell nonlocality, are explored detailedly in the analytical and numerical ways. Each property is witnessed by an appropriate existing criterion. Some of our results are summarized as follows: (i) Large entanglement does not necessarily mean high Wigner negativity and strong Bell nonlocality. (ii) A pure state with a large Schmidt number does not necessarily have a greater Wigner negativity. (iii) Only when $\left\vert\psi _{\left( \theta ,\phi \right) }\right\rangle $ has the Schmidt number 3, the AITTS has the possibility of exhibiting Bell nonlocality in proper parameter range.