  We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the
unfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} >
= | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > |
{\psi_{m\vec{K}}^\mathrm{SC, \beta}} >$ can be decomposed as the sum of the
partial spectral weights $W_{m\vec{K}}^{\mu}(\vec k)$ calculated for each
component $\mu = \alpha, \beta$ independently, effortlessly turning a possibly
complicated problem involving two coupled quantities into two independent
problems of easy solution. Furthermore, we define the unfolding-density
operator $\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds the
primitive cell expectation values $\varphi^{pc}(\vec{k}; \varepsilon)$ of any
arbitrary operator $\mathbf{\hat\varphi}$ according to
$\varphi^{pc}(\vec{k}_{i}; \varepsilon) =
\mathit{Tr}(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \,
\varepsilon)\,\,\hat{\varphi})$. As a proof of concept, we apply the method to
obtain the unfolded band structures, as well as the expectation values of the
Pauli spin matrices, for prototypical physical systems described by
two-component spinor eigenfunctions.
