Qubit Channels and the Bloch Sphere

Visualize the action of common qubit channels on the Bloch sphere.

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Input states are written as \(\rho=\tfrac12(I+\vec r\cdot\vec\sigma)\), with Bloch vector \(\vec r=(r_x,r_y,r_z)\) and \(\|\vec r\|\le 1\). In spherical coordinates, \(r_x=r\sin\theta\cos\phi,\; r_y=r\sin\theta\sin\phi,\; r_z=r\cos\theta\). \(r=1\) is pure and \(0\le r<1\) is mixed. Drag the sphere to rotate the view.

Channel Parameters

Choose a channel family and set its parameters.

Input State

Set \((r,\theta,\phi)\) to choose the input Bloch vector.

Bloch Sphere View

Gray wireframe: Bloch sphere. Orange wireframe: channel image ellipsoid. Blue arrow: input \(\vec r\). Orange arrow: output \(\vec r'\).