Understanding POVM Measurement on Qubit: Placing Detectors & Neumark Extension

[phonon44145]

I have a question about the physical meaning of POVM on a qubit,
F_a = (1/3) (I + n_a$\bullet$$\sigma$) = (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.

 

[naima]

This thread had no answer.
Perhaps now?
in the thread double slit and watching the electrons, i find that the light coming from the slits occurs in two non orthogonal states. they overlap and when the wavelength is equal to the distance between the slits we cannot distinguish them.
has anybody thought about the subject?

 

[naima]

I have found this
it seems to answer to the first post.