Visualizing a Quantum State

Use the sliders to define the quantum state, \(\ket{\psi} = \alpha\ket{0} + \beta\ket{1}\). Adjusting Theta (\(\theta\)) and Phi (\(\phi\)) changes the state's position on the Bloch sphere and updates the complex amplitudes (\(\alpha\) and \(\beta\)) and measurement probabilities in real-time.

State Parameters

0.00

Controls the angle from the North Pole (\(\ket{0}\)).

0.00

Controls the angle around the Z-axis (relative phase).

State Information

\(\alpha\) (Alpha) 1.000 + 0.000i
\(\beta\) (Beta) 0.000 + 0.000i
P(\(\ket{0}\)) = \(|\alpha|^2\) 1.000 (100%)
P(\(\ket{1}\)) = \(|\beta|^2\) 0.000 (0%)

Bloch Sphere