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I understand that one way of creating quantum entangled electrons is by splitting a Cooper pair. Is then their spin property used in the measurement, as this must always sum to $0$?
If that is the case, do quantum entangled electrons only exist in the singlet state, where the spin is always opposite to one another, but not for example the following state? $$\frac{1}{\sqrt{2}}(\left|01\right> + \left|10 \right>)$$ Are there other methods of creating quantum entangled electrons?

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