Fig. 2: Experimental setup for measurement of the q-rms error profile ε_α of measuring process M.

The setup consists of three regions: Blue: preparation of the initial state \(\left|\psi \right\rangle ={(1,0)}^{T}\equiv \left|+z\right\rangle\). Red: preparation of the evolved state \(\left|\psi (t)\right\rangle ={e}^{-{\rm{i}}tA}\left|\psi \right\rangle \to \ \left|\psi (\alpha )\right\rangle ={e}^{-{\rm{i}}t{\sigma }_{x}}\left|\psi \right\rangle ={e}^{({\rm{i}}\alpha {\sigma }_{x})/2}\left|\psi \right\rangle\). Green: Measurement of A², M² and M in state \(\left|\psi (\alpha )\right\rangle\), \(\ \left|\psi (\alpha +\pi )\right\rangle\) and \(\left|+x\right\rangle\), respectively. Projective (sharp) measurements are realized by applying projectors \({P}^{M}(\pm \!\sqrt{2})\) and generalized (unsharp) in terms of POVM by randomized sequences of P^M and \({{\rm{P}}}^{{\sigma }_{x}}\). Bloch spheres above setup indicate the evolution of initial state \(\left|\psi (\alpha )\right\rangle\) and measured projectors P^M and \({{\rm{P}}}^{{\sigma }_{x}}\).