Quantum parameter estimation of non-Hermitian systems with optimal measurements

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 $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Hamiltonian, and give the optimal measurement. Surprisingly, we find some interesting properties of this $\mathcal{P}\mathcal{T}$-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.

arXiv comment13 pages, 7 figures

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• Review: Quantum Metrology and Sensing with Many-Body Systems
• Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
• Critical non-Hermitian topology induced quantum sensing
• Factorization dynamics between quantum Fisher information and quantum coherence
• Experimental investigation of uncertainty relations for non-Hermitian operators
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Noisy Stark probes as quantum-enhanced sensors
• Enhancement of quantum sensing in a dissipatively coupled two-mode system
• Towards Robust Optimal Measurements Against Noise in Quantum Metrology