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Simple question regarding the Bloch Sphere

  1. May 22, 2007 #1
    I am reading Quantum Computation and Quantum Information by Nelson and Chuang myself and came across the Bloch Sphere representation of a quibit on page 15 (equation 1.4) as:

    [tex]|\psi> = \cos\frac{\theta}{2} |0> + e^{i\psi}\sin\frac{\theta}{2} |1>[/tex]

    I have two questions:

    1. What is the motivation behind such a representation (other than the fact that the sum of the squares of the coefficients of [itex]|0>[/itex] and [itex]|1>[/itex] equals 1)?

    2. Why use [itex]\theta/2[/itex] rather than [itex]\theta[/itex]?
     
  2. jcsd
  3. May 22, 2007 #2

    Hurkyl

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    It really is just spherical coordinates.

    I suppose the fact that the parameter space is decomposed into a part that affects measurements in done this basis ([itex]\theta[/itex]) and a part that does not ([itex]\psi[/itex]) is an extra source of convenience.


    Aesthetic reasons. For example, look at expectation calculations. Or maybe the author already gave [itex]\theta[/itex] a meaning, so he has to use this to be consistent.
     
    Last edited: May 22, 2007
  4. May 22, 2007 #3
    Yes, I thought so too, thats why I asked about [itex]\theta/2[/itex]. Thanks.
     
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