Exercise 7.7

Alice’s density matrix is given by Eq. 7.24 in the textbook:

\[ \rho = \begin{pmatrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{pmatrix} \]

\[ \rho^2 = \begin{pmatrix} \frac{1}{4} & 0 \\ 0 & \frac{1}{4} \end{pmatrix} \]

Since \(\rho^2 \ne \rho\), the density matrix represents an entangled state.