  We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of
a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf
S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the
connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by
our earlier work on topological entanglement and the reduced density matrix
$\sigma$ for such link complements, we wanted to determine a choice of Dehn
filling so that the trace of the matrix $\sigma$ becomes equal to the
$\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use
the SnapPy program and numerical techniques to show this equivalence up to the
leading order. We have given explicit results for all hyperbolic knots
$\mathcal{K}$ up to six crossings.
