Fig. 3: Experimental results of projective (sharp) measurement Π1 and generalized (unsharp) measurement Π2.
From: Neutron optical test of completeness of quantum root-mean-square errors
a Bloch sphere depiction of projectors \({{{\Pi }}}_{1}(\pm \!\sqrt{2})={{\rm{P}}}^{M}(\pm \!\sqrt{2})\) of sharp, and POVM elements Π2( ± 2) of unsharp measurement. b Expectations values of \(\left\langle \psi (\alpha )\right|{{{\Pi }}}_{1}(\pm \!\sqrt{2})\left|\psi (\alpha )\right\rangle =\left\langle \psi (\alpha )\right|{{\rm{P}}}^{M}(\pm \!\sqrt{2})\left|\psi (\alpha )\right\rangle\) for projective and \(\left\langle \psi (\alpha )\right|{{{\Pi }}}_{2}({\pm} \!{2})\left|\psi (\alpha )\right\rangle\) for generalized POVM in state \(\left|\psi (\alpha )\right\rangle\) with measurement time tmeas = 100 s. (error-bars represent ±1 st. dev.).
