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Rotation matrix for a Bloch sphere

  1. Jun 23, 2011 #1

    nomadreid

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    Gold Member

    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
    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.
     
  2. jcsd
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