Sequential Stern-Gerlach Experiment

The sequential Stern-Gerlach Experiment applies the same setup as the Stern-Gerlach Experiment sequentially, along different axes. We setup three cases:

Cases

ZZ

We perform a Measurement of the electron spin along the $z$ axis 2 times. After the 1st Measurement, we block all atoms with negative spin $z_{-}$. During the 2nd Measurement all atoms have magnetic moment $z_{+}$.

ZX

We perform a Measurement of the electron spin along the $z$ axis followed by the $x$ axis. After the 1st Measurement, we block all atoms with negative spin $z_{-}$. During the 2nd Measurement, we observe atoms with magnetic moment matching both $x_{+}$ and $x_{-}$.

ZXZ

Similar to the 2nd case, followed by blocking atoms with a $x_{-}$ magnetic moment and adding an extra Measurement of the magnetic moment along the $z$ axis. Since we blocked any atoms with magnetic moment equal to $z_{-}$ after the 1st Measurement, we would expect no such atoms to be seen during the 3rd Measurement. This does not match observations.