Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Three-Outcome Qubit Measurements

Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables in terms of information entropies. The trade-off of the accuracy in the outcome of two successive measurements manifests in entropic noise-disturbance uncertainty relations. Recent theoretical analysis predicts that projective measurements are not optimal, with respect to the noise-disturbance trade-offs. Therefore the results in our previous letter [PRL 115, 030401 (2015)] are outperformed by general quantum measurements. Here, we experimentally test a tight information-theoretic measurement uncertainty relation for three-outcome positive-operator valued measures (POVM), using neutron spin-1/2 qubits. The obtained results violate the lower bound for projective measurements as theoretically predicted.