One example of this is can you measure an electron for up/down spin, then for left/right spin before measuring its quantum partner for left/right spin again? I have tried looking for examples of how this series of measurements would work, but I haven't found anything definitive.
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If you start with an entangled Bell state like $\frac{1}{\sqrt2}(|{\uparrow}{\downarrow}\rangle + |{\downarrow}{\uparrow}\rangle)$, then after your first measurement along the vertical axis, the system will be left in either the state $|{\uparrow}{\downarrow}\rangle$ or the state $|{\downarrow}{\uparrow}\rangle$. Both are unentangled tensor-product states.
If you then measure both electrons along the horizontal axis in either order, you will independently get $|{\leftarrow}\rangle$ or $|{\rightarrow}\rangle$ for each one. There will be no correlation between the outcomes.
benrg
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