  We consider a classical pure SU(2) gauge theory, and make an ansatz, which
separates the space-temporal degrees of freedom from the internal ones. This
ansatz is gauge-invariant but not Lorentz invariant. In a limit case of the
ansatz, obtained through a contraction map, and corresponding to a vacuum
solution, the SU(2) gauge field reduces to an operator, which is the product of
the generator of a global U(1) group times a Pauli matrix. We give a
geometrical interpretation of the ansatz and of the contraction map in the
framework of principal fiber bundles. Then, we identify the internal degrees of
freedom of the gauge field with the non-commutative coordinates of the fuzzy
sphere in the fundamental representation and obtain a one qubit state.
