Errors add up in addition or subtraction. Relative errors add up in multiplication or division. When a quantity is raised to a power, the error is increased by times of the exponent. Now what if the quantity itself is an exponent? What is the rule? $\Delta A=\Delta a∓\Delta b$ for $A=a+b$ or $A=...

Let's say, there is an entangled system of two electrons with opposite spins; The joint system is in a state of eigenvectors for z-Spin ( $S_z$) with both particles far away from each other: $$|\Psi\rangle = \frac{1}{\sqrt{2}}(| +\rangle | -\rangle - |- \rangle | +\rangle)$$ When $S_z$ is measure...