Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

The quantum Cram\'er-Rao bound is a cornerstone of modern metrology, as it provides the ultimate precision in parameter estimation. In multiparameter scenario, this becomes matrix inequality, which can be cast to scalar form with properly chosen weight matrix. Multiparameter estimation thus elicits tradeoffs each estimated. We show that, if information encoded unitary transformation, we naturally choose metric tensor linked geometry underlying algebra $\mathfrak{su}(n)$, applications numerous fields. This ensures an intrinsic that independent choice parametrization.