Threshold size for the emergence of classical-like behavior

In this work we design a procedure to estimate the minimum size beyond which system is amenable classical-like description, i.e. description based on representative points in classical phase-spaces. This obtained by relating quantum states via Generalized Coherent States (GCS), and designing POVM for GCS discrimination. Conditions upon discrimination are defined, such that results convey enough information meet our needs reliability precision, as gauged two parameters $\epsilon$, of arbitrary choice, $\delta$, set experimental apparatus, respectively. The implies definition what meant "size" system, terms number $N$ elementary constituents provide global algebra leading phase-space emergent description. above conditions can be thus turned into $N>N_{\rm t}(\epsilon,\delta)$, where $N_{\rm t}(\epsilon,\delta)$ threshold mentioned title. specific case magnetic considered, with details gedanken experiment presented thoroughly commented. Results pseudo-spin bosonic systems also given.