Abstract
A
bstract
We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in
SU
(2)
1
Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions, enabling an explicit topological realization of
W
n
and Dicke states, as well as their entanglement properties. For the genus-1 case, the modular
SL
(2
,
ℤ) generators on a single torus boundary realize the standard Clifford generators. We further conjecture a higher-genus extension of this correspondence specifically for the Clifford orbits of
W
and Dicke states, in which the orbit of
W
n
is represented by a sum over genus-
g
handlebodies with Dehn twists applied to each torus. Our results extend the known correspondence between Clifford structures and modular transformations, and demonstrate that non-stabilizer states can be understood as controlled deformations within the
SU
(2)
1
modular tensor category, providing a concrete example of how non-stabilizer quantum resources emerge from purely topological data.