Physics Asked by forpointing on December 4, 2020
If we have a normalized entagled state:
$$ |arangle=N (|1rangle|2rangle+|1rangle|-2rangle+|1rangle|2rangle-|-1rangle|2rangle) $$
Where $|2rangle, |-2rangle$ describes particles A and $|1rangle, |-1rangle$ particle B.
If we measure this system and find out that particle A is in the state $|2rangle$, the system will be in a superposition of the states $|1rangle|2rangle$ and $|-1rangle|2rangle$, right?
How can we write this new state?
Did you mean your state is $$|1rangle|2rangle+|1rangle|-2rangle+|-1rangle|-2rangle+|-1rangle|2rangle $$ (an even superposition of all states)?
In that case, yes, you will have a state that is a superposition of $1rangle|2rangle$ and $|-1rangle|2rangle $.
You can write the new normalized state as $frac{1}{sqrt{2}} 1rangle|2rangle + frac{1}{sqrt{2}}|-1rangle|2rangle$.
Answered by nosuchthingasmagic on December 4, 2020
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