Exploring topological entanglement through Dehn surgery

We compute the PSL(2,C) Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement S³ L, where L=K# H is the connected sum of the knot K with the Hopf link H. Motivated by our earlier work on topological entanglement and the reduced density matrix σ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix σ becomes equal to the PSL(2,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 K up to six crossings.