Covariant correlation-disturbance and its experimental realization with spin-1/2 particles

Abstract

We formulate a precise tradeoff relation between correlation and disturbance for sequential $n$-outcome quantum measurements in Hilbert spaces of arbitrary dimension. This relation highlights key symmetry properties useful for robust estimation and characterization of the measurement parameters against unitary noise, or in scenarios where shared reference frames are unavailable. In addition, we report on the experimental implementation of the proposal for the qubit case, more precisely in a neutron optical experiment, which is particularly valuable for calibrating and optimizing measurement devices, as confirmed by the theoretical results. Finally, we exploit the optimal tradeoff relation for direct estimation of the characteristic noise of single-photon detectors, dark counts, and the finite detection efficiency.