The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors | 0 ⟩ ⟩ and | 1 ⟩ ⟩ , respectively, which in turn might correspond e.g. to the spin -up and spin -down states of an electron. This choice is arbitrary, however. The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states. The Bloch sphere may be generalized to an n -level quantum system, but then the visualization is less useful.