从扩张厄米性中提取内部非定域性
Extracting the internal nonlocality from the dilated Hermiticity
摘要：
为了有效地实现一个$\cal PT$ -对称系统，可以将一个$\cal PT$ -对称哈密顿量扩张为某个整体的厄米算符，并模拟其在扩张厄米算符系统中的演化.然而，只有一个整体的厄米哈密顿量，我们如何知道它是否是一个膨胀，是有用的模拟？为了回答这个问题，我们考虑如何提取厄米膨胀中的内部非定域性的问题。我们揭示了内部非局域性带来的子系统之间的非平凡的相关性。通过评估在三个不同的图片与本地测量的相关性，由此产生的不同期望的贝尔运营商揭示了内部非局域性的区别。当模拟的$\cal PT$对称哈密顿量接近其例外点时，这种区别往往是最显着的。我们的结果清楚地使埃尔米特膨胀和其他全球的哈密顿没有内部非局域性之间的差异。它们还提供品质因数来测试仿真的可靠性，以及验证$\cal PT$对称（子）系统。
英文摘要：
To effectively realize a $\cal PT$-symmetric system, one can dilate a $\cal PT$-symmetric Hamiltonian to some global Hermitian one and simulate its evolution in the dilated Hermitian system. However, with only a global Hermitian Hamiltonian, how do we know whether it is a dilation and is useful for simulation? To answer this question, we consider the problem of how to extract the internal nonlocality in the Hermitian dilation. We unveil that the internal nonlocality brings nontrivial correlations between the subsystems. By evaluating the correlations with local measurements in three different pictures, the resulting different expectations of the Bell operator reveal the distinction of the internal nonlocality. When the simulated $\cal PT$-symmetric Hamiltonian approaches its exceptional point, such a distinction tends to be most significant. Our results clearly make a difference between the Hermitian dilation and other global Hamiltonians without internal nonlocality. They also provide the figure of merit to test the reliability of the simulation, as well as to verify a $\cal PT$-symmetric (sub)system.
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