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However if we apply this to the triplet state [tex]\frac{1}{\sqrt{2}}(\mid+-\rangle+\mid-+\rangle)[/tex].

we find the following :

suppose we measure spin A with result +, then spin B is - (we see this by the projection on the possible state), however it's a state with total spin 1, since this triplet state is eigenvector of the sum operator (S1+S2)^2.

So we fing that the following is different : measuring spin A and then spin B and making the sum,

or making the measurement of the sum. How does the system know in advance the sum will be taken ?