Solution
= Solution
\b[The state is separable.] The <identity matrix> resolves into the four projectors of the <computational basis>, giving the explicit <quantum state ensemble>
$$
\boxed{\frac{I_4}{4}=\frac14\sum_{i,j=0}^1
\bigl(|i\rangle\langle i|\bigr)_A\otimes\bigl(|j\rangle\langle j|\bigr)_B
=\frac{I_2}{2}\otimes\frac{I_2}{2}.}
$$
Each member is a <pure state> that is a <product state>, so this is a <separable quantum state> by its defining decomposition.