case [@toscano], with the relevant difference that here in the PT case they decay very quickly. The oscillations for larger $\lambda$ are shown in the enlarged view in the lower inset of Fig. \[plot\]. This decay of the overlap oscillations is due to the fact that for physical systems with SU(1,1) or SU(2) algebras as our PT system, a displaced coherent state does not remain a coherent state, due to the higher order terms in the Baker-Campbell-Hausdorff development of the displacement operator. Therefore, the larger the displacement $\lambda$, the more distorted the coherent state, implying that the overlap is always close to zero when the displacement is not small. The HO instead obeys the Heisenberg–Weyl algebra ($[a,a^{\dagger}]=1$) and the displaced coherent state is still a coherent state, so that the overlap oscillations decay much more slowly. However the important point of our result is that, even though only one or two oscillations are visible, the period of oscillation, which gives the scale of quasi-orthogonality, is extremely small. This means that the PT system is very sensitive to phase-space displacement. Moreover this sensitivity is due just to the sub-Planck structures of the compass-state. In fact, the period of the overlap oscillation 