  Entanglement is an important concept in quantum information, quantum
communication, and quantum computing. We provide a geometrical analysis of
entanglement and separability for all the rank-2 quantum mixed states: complete
analysis for the bipartite states, and partial analysis for the multipartite
states. For each rank-2 mixed state, we define its unique Bloch sphere, that is
spanned by the eigenstates of its density matrix. We characterize those Bloch
spheres into exactly five classes of entanglement and separability, give
examples for each class, and prove that those are the only classes.
