Classical motion conjecture for continuously observed quantum blobs

A quantum blob is a phase-space set denoted by $\mathcal{QB}^{2n}$. Let $f_t^H$ be the classical Hamilton flow associated with a Hamiltonian $H$, and let $t$ be the observation time. Classical motion conjecture. When we continuously observe the motion of a quantum blob, an initial quantum blob $\mathcal{QB}^{2n}$ is transformed into

$$f_t^H(\mathcal{QB}^{2n}).$$

Thus, continuous observation reveals the classical Hamiltonian motion of the blob. This conjecture extends the stated classical evolution result for quadratic Hamiltonians to arbitrary physical Hamiltonians, for which the approximation is expected to remain excellent over generically large Ehrenfest times.