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    This study links quantum metrology resolution with quantum coherence. A quantum Wiener-Khintchine theorem is developed for a quantum ruler, balancing probe and measurement contributions in linear metrology.

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    Area of Science:

    • Quantum Physics
    • Metrology
    • Information Theory

    Background:

    • Quantum coherence is crucial for advanced quantum technologies.
    • Understanding the interplay between coherence and measurement resolution is key.
    • Existing metrological frameworks may not fully capture quantum effects.

    Purpose of the Study:

    • To establish a clear relationship between quantum metrological resolution and quantum coherence.
    • To develop a generalized quantum framework for metrological analysis.
    • To explore the role of probe and measurement in quantum sensing.

    Main Methods:

    • Development of a quantum version of the Wiener-Khintchine theorem.
    • Modeling a quantum ruler to analyze metrological performance.
    • Application to various linear metrology scenarios.

    Main Results:

    • Demonstrated a direct link between quantum coherence and metrological resolution.
    • The developed quantum theorem treats probe and measurement contributions equally.
    • Successfully applied the framework to diverse linear metrology examples.

    Conclusions:

    • Quantum coherence fundamentally dictates metrological precision.
    • The quantum Wiener-Khintchine theorem offers a unified approach to quantum metrology.
    • This work provides a foundation for enhanced quantum sensing and measurement techniques.