Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Spin-1/2 Measurements

Information-theoretic definitions for noise and disturbance in quantum measurements were given in [Phys. Rev. Lett. 112, 050401 (2014)] and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight noise-disturbance uncertainty relation for complementary qubit observables and carry out an experimental test. Successive projective measurements on the neutron's spin-1/2 system, together with a correction procedure which reduces the disturbance, are performed. Our experimental results saturate the tight noise-disturbance uncertainty relation for qubits when an optimal correction procedure is applied.