The exact information cost of randomized measurements in quantum metrology

arXiv:2611.00599v1 Announce Type: new Abstract: Randomized measurements provide state-independent readout for multiparameter quantum sensing. Although 3-designs retain a constant fraction of the quantum Fisher information (QFI) for every pure state, we show that 2-designs need not. In dimension \(d\), complete mutually unbiased bases (MUBs) retain exactly \(1/(d+1)\) of the QFI in the worst state and direction, attaining the universal lower bound for 2-designs built from orthonormal bases; symmetric informationally complete (SIC) measurements retain exactly \((1-1/\sqrt{d+1})/d\). The loss comes from aligned blind spots. Relative to a basis, pure-state changes split into population and phase parts of equal dimension, but probabilities respond only to the former.