Non-Hermitian effects on the quantum parameter estimation in pseudo-Hermitian systems Article Swipe

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Lin Wei , Haijun Xing , Libin Fu , H. D. Liu ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2505.19079

Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian systems. By employing the projected Hilbert space method and spectral decomposition, we derive an explicit expression for the QFI in terms of the density matrix and parameter generators. This formulation not only recovers the well-known results in the Hermitian case but also captures the non-Hermitian effects induced by the time-dependent norm of the state. To validate our theoretical framework, we analyze a single-qubit pseudo-Hermitian system and apply Naimark dilation theory to embed it into an equivalent Hermitian system. The comparison between the original and dilated systems demonstrates the consistency and applicability of the proposed QFI formula in non-Hermitian settings. In addition, we investigate a $\mathcal{PT}$-symmetric system to further explore the influence of non-Hermiticity on QFI. Our findings offer a new perspective for analyzing and enhancing QFI in non-Hermitian systems, paving the way for promising applications in non-Hermitian quantum metrology and sensing.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2505.19079
PDF: https://arxiv.org/pdf/2505.19079
OA Status: green
OpenAlex ID: https://openalex.org/W4414585600

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DOI: https://doi.org/10.48550/arxiv.2505.19079

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Title: Non-Hermitian effects on the quantum parameter estimation in pseudo-Hermitian systems

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-05-25

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Authors: Lin Wei, Haijun Xing, Libin Fu, H. D. Liu

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Landing page: https://arxiv.org/abs/2505.19079

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PDF URL: https://arxiv.org/pdf/2505.19079

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Cited by: 0

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