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The key to figuring out the probability of any measurement result is Born's rule, which says that if you have a state $\left|\psi\right\rangle$ the probability of observing measurement outcome $\left|\phi\right\rangle$ is given by $$ \begin{align} \Pr(\phi | \psi) = \left|\left\langle \phi | \psi \right\rangle \right|^2. \end{align} $$ In the example you ...


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