For a one-qubit system, a general pure state can be written as a linear combination of and :
where and . When interpreted as the polar and azimuthal angles in spherical polar coordinates, the angles and uniquely identify a point on a unit sphere called the Bloch sphere. With the one-to-one correspondence between the points on the Bloch sphere and the pure state space of a one-qubit system, the Bloch sphere can be used to visualize any pure state of a one-qubit system.
Bloch Sphere by Eckher provides an interactive way to visualize the pure one-qubit states on the Bloch sphere by manipulating the and angles as well as pseudo-rotating the sphere by clicking/touching and dragging.