Experimental test of entropic noise-disturbance uncertainty relations for three-outcome qubit measurements

Abstract

Information-theoretic uncertainty relations formulate the joint immeasurability of two noncommuting observables in terms of information entropies. The tradeoff 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 tradeoffs. Therefore, the results in our previous paper [Phys. Rev. Lett. 115, 030401 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.030401] are outperformed by general quantum measurements. Here, we experimentally test a tight information-theoretic measurement uncertainty relation for three-outcome positive-operator-valued measures, using neutron spin-1/2 qubits. The obtained results violate the lower bound for projective measurements as theoretically predicted.