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If I had to summarize quantum teleportation in one equation, I would write $$ |\psi\rangle \otimes |\beta_{00}\rangle = \displaystyle \frac{1}{2} \sum_{z,x \in \{0,1\}} |\beta_{zx}\rangle \otimes X^x Z^z |\psi\rangle $$ You can verify this by explicitly writing out all terms on the right-hand side. Here $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ ...



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