Linear dependence among the diagonal components of Hamiltonian derivatives creates a slow parameter direction with O(t^0) scaling, obstructing simultaneous t^{-2} multiparameter quantum estimation.
A full-rank weight matrix can always be decomposed asW= MT Mfor some invertible matrixM
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Geometric obstructions to quadratic time scaling in multiparameter quantum estimation
Linear dependence among the diagonal components of Hamiltonian derivatives creates a slow parameter direction with O(t^0) scaling, obstructing simultaneous t^{-2} multiparameter quantum estimation.