Abstract
Abstract Weak value amplification is crucial in quantum metrology because it enhances the detection of subtle interactions between quantum entities. However, current weak value quantum metrology techniques are only effective for extremely weak interactions, significantly narrowing its range of potential applications. 
In this work, we present the `metrological weak value,' designed for use with quantum interactions of any strengths, making it unnecessary to have prior knowledge of how strong or weak a quantum interaction might be.
Additionally, we demonstrate an adaptive estimation scheme for weak value quantum metrology tailored for gauging an undetermined interaction strength. This scheme, rooted in metrological weak value measurements, aligns perfectly with the quantum Cramér-Rao lowest bound. 
The versatility and effectiveness of the metrological weak value enables weak value quantum metrology beyond weak interactions, paving the way for precision in quantum measurement and broadening its utility across various quantum systems.
Published Version
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