Solution (source code)

= Solution

The four <Bell states> form an orthonormal basis, so their uniform mixture is
$$
\rho=\frac{I_4}{4}
=\frac{I_2}{2}\otimes\frac{I_2}{2}.
$$
It is a product state and therefore
$$
\boxed{\operatorname{SN}(\rho)=1}.
$$