arXiv subjects

Bing-Shu Hu

Publications and source records attributed to Bing-Shu Hu.

3 recordsLinked to original sources

arXiv2026

Quantifying Uhlmann curvature from Yang-Mills action and its implications in quantum multiparameter estimation

The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum states is still an open problem. Inspired by the Yang-Mills action in non-Abelian gauge theory, we propose a scalar quantifying the Uhlmann curvature and establish its connection to the measurement incompatibility in quantum multiparameter estimation problems. We show that this curvature measure is gauge invariant, reparametrization invariant, and vanishes if and only if the Uhlmann curvature vanishes. We also explicitly calculate the Uhlmann curvature for the joint estimation of phase and phase diffusion as an example.

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arXiv2025

Quantum Parameter Estimation Uncertainty Relation

Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter correlation. By strategically manipulating the multidimensional parameter space, we derive an estimation uncertainty relation that quantifies how these factors jointly limit estimation precision in the two-parameter case. This uncertainty relation is tight for pure states and thus completely describes the quantum limit of two-parameter estimation precision in a simple inequality. To intuitively illustrate the impact of the uncertainty relation, we develop an error-ellipse method and demonstrate its utility in phase-space displacement estimation. Our results reveal that a geometric perspective of the parameter space offers a powerful approach for addressing multiparameter estimation challenges.

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arXiv2025

Revisit on quantum parameter estimation approach for Mach-Zehnder interferometry

The Mach-Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths, serving as a crucial prototype for achieving high-precision measurements in various scientific and technological applications. In this study, we analyze different models for estimating relative phase shift in a general two-arm Mach-Zehnder interferometer. We demonstrated that single-parameter estimation models can be reduced from the two-parameter estimation model by imposing appropriate constraints on the parameter space. To make quantum Fisher information of the single-parameter estimation models meaningful, the corresponding constraints must be guaranteed in the experiment implementation. Furthermore, we apply the quantum Fisher information approach to analyze the Mach-Zehnder interferometer with the an input state composed of a displaced squeezed vacuum state and a coherent state, providing insights into the precision limits of such configurations.

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