Solution
= Solution
In the computational product bases, the coefficient matrix is
$$
C=\frac1{\sqrt3}\begin{pmatrix}1&1\\1&0\end{pmatrix}.
$$
Its determinant is $-1/3$, so it has rank two. Therefore \b[the Schmidt number is $\boxed{2}$.] As a check, the reduced density operator $CC^\dagger=\frac13\begin{pmatrix}2&1\\1&1\end{pmatrix}$ has eigenvalues $(3+\sqrt5)/6$ and $(3-\sqrt5)/6$, both positive.