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arXiv · 2605.23514

Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation

Lingna Wang·Hongzhen Chen·Haidong Yuan
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Abstract

A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum limits. Here, we present an approach that precisely quantifies these trade-offs for an arbitrary number of parameters encoded in pure quantum states. Our approach not only derives tight analytical bounds for the trade-offs induced by measurement incompatibility but also provides a systematic methodology to design optimal measurement strategies that saturate these limits. To demonstrate the practical significance of our findings, we apply our framework to quantum radar and obtain a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity with any given amount of entanglement. This showcases the transformative potential of our findings for a wide range of applications in quantum metrology, sensing, and beyond.

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Lingna Wang, Hongzhen Chen, Haidong Yuan. 2026-05-22. Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation. https://doi.org/10.1103/dvj7-9thf

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