If Alice receives she measures in the and if she gets she outputs 0 computational basis \(|0\rangle\) 0 0 computational basis \(|1\rangle\) 1 1 sign basis \(|+\rangle\) 0 1 sign basis \(|-\rangle\) 1 // Two equivalent methods of measuring in the computational basis Measure([PauliZ], [qubit]); M(qubit); // Measuring in the sign basis Measure([PauliX], [qubit]); $$ \sigma_z|0\rangle = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \end{bmatrix} = 1|0\rangle $$ $$ \sigma_z|1\rangle = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ -1 \end{bmatrix} = -1|1\rangle $$ $$ \sigma_x|+\rangle = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} \frac{1}{\sqrt{2}} \\…