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arXiv · 2506.15352

Quantum Parameter Estimation Uncertainty Relation

Bing-Shu Hu·Xiao-Ming Lu
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Abstract

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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Bing-Shu Hu, Xiao-Ming Lu. 2025-06-18. Quantum Parameter Estimation Uncertainty Relation. https://arxiv.org/abs/2506.15352

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