论文标题
具有最佳测量的非热系统系统的量子参数估计
Quantum parameter estimation of non-Hermitian systems with optimal measurements
论文作者
论文摘要
使用Hermitian系统的量子参数估计已应用于各个领域，但是关于非炎性系统的结果相对较少。在这里，我们研究了一般非热汉密尔顿人的量子参数估计，并得出了纯状态的量子Fisher信息（QFI）的直观表达。此外，我们提出了最佳测量的条件，该条件适用于Hermitian和非炎症的哈密顿人。为了说明这些结果，我们计算和研究了特定$ \ Mathcal {pt} $ - 对称的非hermitian Hamiltonian的QFI，并进行最佳测量。令人惊讶的是，我们发现了此$ \ Mathcal {pt} $ - 对称的Hamiltonian QFI的一些有趣属性，例如ep的QFI中的突变。此外，我们还比较了最佳测量结果与理论精度所产生的估计的差异，以验证我们提出的最佳测量条件。
Quantum parameter estimation with Hermitian systems has been applied in various fields, but there are relatively few results concerning non-Hermitian systems. Here, we study the quantum parameter estimation for general non-Hermitian Hamiltonians and derive an intuitive expression of quantum Fisher information (QFI) for pure states. Furthermore, we propose the condition for optimal measurements, which is applicable to both Hermitian and non-Hermitian Hamiltonians. To illustrate these results, we calculate and study the QFI of a specific $\mathcal{PT}$-symmetric non-Hermitian Hamiltonian, and give the optimal measurement. Surprisingly, we find some interesting properties of this $\mathcal{PT}$-symmetric Hamiltonian QFI, such as the mutations in QFI at EP. Moreover, we also compare the variance of estimation generated by the optimal measurement with the theoretical precision bound to verify the condition for optimal measurements we proposed.
