Pure Qubit Question: Does Alice Fulfill Bob's Demand?

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begyu85
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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..?
 
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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

Jim Graber
 
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... ?