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Pure qubit question

  1. Apr 30, 2008 #1
    Hi,

    One can describe a pure qubit in two ways (onto the bloch-sphere): 1.) one take a ([tex]\alpha,\beta[/tex]) , where [tex]\alpha,\beta[/tex] are complex numbers and [tex]\left|\alpha\right|^{2}+\left|\beta\right|^{2}=1[/tex]. 2.) with a real 3-dimensional unit vector.

    Bob wants that Alice generate one million random ([tex]\alpha,\beta[/tex]) qubit to him. Alice generates rather one million real unit vectors and after this she enumerates this unit vectors to ([tex]\alpha,\beta[/tex]) one by one.

    My question is: Did Alice fulfill Bob's demand? Are Bob going to accept Bob's qubits..?
     
  2. jcsd
  3. Apr 30, 2008 #2

    jimgraber

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    Gold Member

    How did Alice generate those "random" 3D real unit vectors?
    How does Bob generate random alpha beta pairs?
    I assume you want uniform coverage of the Bloch sphere in both cases.
    If so, Bob should not be able to tell the difference.
    Just my $.02
    Best,
    Jim Graber
     
  4. Apr 30, 2008 #3
    Yes, the distribution of the random qubits is uniform...

    My first thought was this what you are saying...but is this answer correct? I mean this would be so simple...

    In the first case i will get some statistics, and i have to transform to an other one.. Question: does this transformation (between the representation of the qubits) preserve the features of the statistics... ?
     
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