I have a question about the physical meaning of POVM on a qubit, F_a = (1/3) (I + n_a[itex]\bullet[/itex][itex]\sigma[/itex]) = (2/3) E(n_a) where E(n_a) is a projector on n_a direction, and 3-vectors n_a satisfy n_1+n_2+n_3=0 Does it mean that you actually put 3 detectors along n_1,n_2, and n_3, and wait for one of them to click? I find the question about detector placement totally confusing in view of the fact that any Stern-Gerlach apparatus can only resolve spin-up vs. spin-down, i.e. two orthogonal states. One of the literature sources I've read contained a very vague hint that the physical placement of detectors does not correspond to the n_1,n_2,n_3 directions, but the authors did not elaborate any further. Can anyone confirm or refute that, and explain where in fact one must put the detectors to make a POVM measurement? I am not asking about the Neumark extension to a qutrit. I just want to know how to set up a POVM measurement on a single qubit that is not coupled to any ancillas. Any feedback is appreciated.