Bloch Sphere

A block sphere is a geometric interpretation of the pure state space of a two-state quantum mechanical system (qubit). It is named after the physicist Felix Bloch.

Quantum mechanics is mathematically formulated in the Hilbert space or the projective Hilbert space. The pure states of a quantum system correspond to one dimensional subspaces of the corresponding Hilbert space (and the "points" of the projective Hilbert space). For a two dimensional Hilbert space, the space of all such states is the complex projective line \(\Bbb{CP}_1\). This is the Bloch Sphere, which can be mapped to the Reimann sphere.