Related papers: Quantum parameter estimation of non-Hermitian systems with optimal measurements

Quantum parameter estimation of non-Hermitian systems with optimal measurements

URL: http://arxiv.org/abs/2208.05159v3
Date: Mon, 4 Sep 2023 08:47:36 GMT
Title: Quantum parameter estimation of non-Hermitian systems with optimal measurements
Authors: Xinglei Yu, Chengjie Zhang
Abstract summary: We study the quantum parameter estimation for general non-Hermitian Hamiltonians. We propose the condition for optimal measurements, which is applicable to both Hermitian and non-Hermitian Hamiltonians.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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