In a network of spin $\frac{1}{2}$ particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that characterizes the interaction of the spin with the external control field. Multipartite networks are such that the spins are divided into subsets according to their gyromagnetic ratio and spins in one set interact in the same way with all spins in another set. Due to the presence of symmetries in these types of systems, the underlying Hilbert state space splits into invariant subspaces for the dynamics. Subspace controllability is verified if every unitary evolution can be generated by the dynamics on these subspaces.

We give an exact characterization, in terms of graph theoretic conditions, of subspace controllability for multipartite quantum spin networks. This extends and unifies previous results.

在自旋网络中 $\frac{\mathrm{1个}}{\mathrm{2个}}$通过外部电磁场控制粒子，每个自旋的旋磁比是表征自旋与外部控制场相互作用的参数。多部分网络使得自旋根据其旋磁比被分成子集，并且一组中的自旋以相同的方式与另一组中的所有自旋相互作用。由于这些类型的系统中存在对称性，因此基础的希尔伯特状态空间分裂为动力学的不变子空间。如果可以通过这些子空间上的动力学生成每个单位演化，则可以验证子空间的可控性。

根据图论条件，我们给出了多部分量子自旋网络的子空间可控性的精确表征。这扩展并统一了以前的结果。