Quantifying Quantum Uncertainty Via Metric‐Adjusted Skew Information and Symmetric Measurements

Quantum entanglement and coherence, serving as cornerstone resources for quantum information science, fundamentally depend on quantum measurements for their detection and quantification, with quantum uncertainty serving as the essential link that connects these components. In this work, by integrating metric‐adjusted skew information with informationally complete symmetric measurements, we establish a universal connection between measurement‐induced quantum uncertainty and the fundamental quantum uncertainty measure. Then, we demonstrate that the total uncertainty associated with symmetric measurements is universally proportional to the intrinsic quantum uncertainty of the state. Subsequently, we derived a series of entanglement criteria by employing the proposed framework and demonstrated their validity and comprehensiveness through illustrative example. In addition, we employ symmetric measurements with metric‐adjusted skew information to formulate generalized measures of average coherence, and derive several measurement‐based complementary trade‐off relations for average coherence associated with a given quantum state. This framework offers a robust quantitative approach to understanding quantum resources, with significant practical implications for the analysis of quantum entanglement and coherence.