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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.

Aidan
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    You can measure anything you want to. – WillO Jun 11 '22 at 00:32
  • just to be clear, with no previous measurements, the first verticle measurement would have a 50/50 chance of being up or down, then the horizontal measurement would have a 50/50 chance of being left or right because it would be at 90 degrees to the verticle measurement. then after all of this if you measured the other entangled particle horizontally then it would be exactly opposite to the horizontal measurement of the other. – Aidan Jun 11 '22 at 02:08
  • see my simple example of "entanglement" here https://physics.stackexchange.com/questions/439450/how-do-we-know-quantum-entanglement-works-no-matter-the-distance/439469#439469 . Each measurement is a quantum mechanically controlled interaction, and an individual electron will give a probability point for a spin distribution , so I think any information on individual interactions will be lost. – anna v Jun 11 '22 at 03:11
  • so what would be the actual probabilities if you measured an electron for verticle spin, then for horizontal spin, and then measure its quantumly entangled partner for horizontal spin? – Aidan Jun 11 '22 at 03:32
  • there would be no measurement of entanglement, when you measure the first electron and find its spin, for the conservation laws you will know the spin of the other. To measure at the same time, not consecutively (your "then") it cannot be done, two entangled electrons , coming from the same vertex of interaction , would need a specially designed experiment, and it would just show the spin distributions. – anna v Jun 11 '22 at 03:49

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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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  • if you measured vertically again would the states be in an entangled bell state again? – Aidan Jun 11 '22 at 05:24
  • would measuring the position of one of the electrons put it back in an entangled bell state because of the Heisenberg uncertainty printable? – Aidan Jun 11 '22 at 05:53
  • @Aidan You can't entangle particles by doing things to them independently, so the answer to both questions is no. After the first measurement, the particles don't "remember" that they used to be entangled. – benrg Jun 11 '22 at 07:10