  Quark-hadron continuity is a scenario that hadronic matter is continuously
connected to color superconductor without phase transitions as the baryon
chemical potential increases. This scenario is based on Landau's classification
of phases since they have the same symmetry breaking pattern. We address the
question whether this continuity is true as quantum phases of matter, which
requires the treatment beyond Ginzburg-Landau description. To examine the
topological nature of color superconductor, we derive a dual effective theory
for $U(1)$ Nambu-Goldstone (NG) bosons and vortices of the color-flavor locked
phase, and discuss the fate of emergent higher-form symmetries. The theory has
the form of a topological $BF$ theory coupled to NG bosons, and fractional
statistics of test quarks and vortices arises as a result of an emergent
$\mathbb Z_3$ two-form symmetry. We find that this symmetry cannot be
spontaneously broken, indicating that quark-hadron continuity is still a
consistent scenario.
