We investigated the dynamics of quantum Fisher information for a two-level system controlled by a non-Hermitian operation under the depolarization, and the non-Hermitian operation is described by a special Hamiltonian in which both the \(\mathcal {PT}\)-symmetric zone and the \(\mathcal {PT}\)-symmetry broken zone are considered. Our results show that the non-Hermitian operation can effectively control the evolutionary behavior of quantum Fisher information of the system. Especially, through a proper choice of the non-Hermiticity parameter combining with the optimal input state and a low depolarizing probability, quantum Fisher information of the system can be significantly increased by the non-Hermitian operation. According to the quantum Cramér–Rao inequality, the inverse of quantum Fisher information provides the lower bound of the error of the parameter estimation. Our investigation also shows that the non-Hermiticity in the operation which is performed on the initial state is robust against the depolarizing decoherence, and the precision of parameter estimation can be remarkably enhanced by applying an appropriate non-Hermitian operation.

中文翻译：

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去极化下非赫米特操作控制的两层系统的量子Fisher信息

我们研究了在去极化作用下由非赫米特操作控制的两层系统的量子Fisher信息的动力学，并且非赫米特操作由特殊的哈密顿量描述，其中\（\ mathcal {PT} \不对称区域和\（\ mathcal {PT} \）考虑对称破损区。我们的结果表明，非Hermitian运算可以有效地控制系统的量子Fisher信息的演化行为。特别地，通过适当地选择非赫米特性参数并结合最佳输入状态和低去极化概率，可以通过非赫米特操作显着增加系统的量子费希尔信息。根据量子Cramér-Rao不等式，量子Fisher信息的逆提供了参数估计误差的下界。我们的研究还表明，在初始状态下执行的操作中的非赫米蒂性对于去极化退相干具有很强的抵抗力，