For an unknown finite group $G$ of automorphisms of a finite-dimensional Hilbert space, we find sharp bounds on the number of generic $G$-orbits needed to recover $G$ up to group isomorphism, as well as the number needed to recover $G$ as a concrete set of automorphisms.

翻译：对于一个未知的有限群$G$（作用于有限维希尔伯特空间的自同构群），我们给出了精确的界：需要多少个一般性的$G$轨道才能重构出$G$的群同构类，以及需要多少个轨道才能将$G$重构为具体的自同构集合。