Quantization of birational symplectomorphisms of algebraic tori

Let ${\bf k}$ be an algebraically closed field of characteristic zero, let $\mathbb G_{m,\bf k}^{2n}$ carry the standard symplectic form

$$\sum_{i,j\leq 2n}\omega_{ij}(x_i^{-1}dx_i)\wedge(x_j^{-1}dx_j),$$

and let $BirSympl_{n,\bf k}$ be the group of its birational symplectomorphisms. Quantum-torus quantization conjecture. There exists a homomorphism from $BirSympl_{n,\bf k}$ to the group of outer automorphisms of the skew field of fractions of the quantum torus. Its semiclassical limit as $q\to1$ exists and gives the identity map on the corresponding group of birational symplectomorphisms of the algebraic torus. This is presented as the quantum-torus analogue of a conjecture from the cited work of Kontsevich and Kaledin; the source does not establish existence or the stated limit.