Reading about the general rotation of a single qubit, a rotation of [itex]\theta[/itex] in the horizontal plane and [itex]\phi[/itex]) in the vertical plane, is given as the matrix(adsbygoogle = window.adsbygoogle || []).push({});

V( [itex]\theta[/itex] , [itex]\phi[/itex]) =

cos([itex]\theta[/itex]/2) .................-i[itex]e^{-i \phi}[/itex] sin([itex]\theta[/itex]/2)

-i[itex]e^{i\phi}[/itex] sin([itex]\theta[/itex]/2)...........cos([itex]\theta[/itex]/2)

(The dots are just spacing.)

Which would make sense to me except that I do not understand why the 1/2 factor for the angle in the horizontal plane is there. Could someone explain that for me? Thanks.

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# Rotation matrix for a Bloch sphere

Can you offer guidance or do you also need help?

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