There are various statements in the physics literature about the stratification of quantum states, for example into orbits of a unitary group, and about generalized differentiable structures on it. Our aim is to clarify and make precise some of these statements. For A an arbitrary finite-dimensional C*-algebra and $U(A)$ the group of unitary elements of A, we observe that the partition of the state space $\mathcal{S}(A)$ into $U(A)$ orbits is not a decomposition and that the decomposition into orbit types is not a stratification (its pieces are not manifolds without boundary), while there is a natural Whitney stratification into matrices of fixed rank. For the latter, when A is a full matrix algebra, we give an explicit description of the pseudo-manifold structure (the conical neighborhood around any point). We then make some comments about the infinite-dimensional case.

物理学文献中有各种关于量子态分层的陈述，例如划分为酉群的轨道，以及关于其上的广义可微结构。我们的目标是澄清并准确地做出这些陈述中的一些。对于A任意有限维 C*-代数和$你(\mathrm{一种})$A的酉元素群，我们观察到状态空间的划分$\mathcal{秒}(\mathrm{一种})$ 进入 $你(\mathrm{一种})$轨道不是分解，并且分解为轨道类型不是分层（它的部分不是没有边界的流形），而有一个自然的惠特尼分层到固定秩的矩阵。对于后者，当A是全矩阵代数时，我们给出了伪流形结构（任何点周围的圆锥邻域）的明确描述。然后我们对无限维情况做一些评论。