  We explore a web of connections between quantum entanglement and knot theory
by examining how topological entanglement entropy probes the braiding data of
quasi-particles in Chern-Simons theory, mainly using $SU(2)$ gauge group as our
working example. The problem of determining the Renyi entropy is mapped to
computing the expectation value of an auxiliary Wilson loop in $S^3$ for each
braid. We study various properties of this auxiliary Wilson loop for some
2-strand and 3-strand braids, and demonstrate how they reflect some geometrical
properties of the underlying braids.
