Semiclassical equivalence conjecture for geometric quantizations

Let $(M,\omega)$ be a closed symplectic manifold. A geometric quantization is a sequence of maps $\{T_k:C^\infty(M)\to\mathcal{L}(H_k)\}_{k\in\mathbb{N}}$ satisfying the geometric quantization axioms, where $H_k$ are Hilbert spaces. Semiclassical equivalence conjecture. Two geometric quantizations of $(M,\omega)$ associated with sequences of Hilbert spaces of the same dimension are semiclassically equivalent; that is, after conjugation by a sequence of unitary operators, their quantization maps agree to order $O(1/k)$ on every fixed smooth function. This generalizes the established equivalence results for the sphere and torus to arbitrary closed symplectic manifolds, while the general case remains open.