Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook