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

[begyu85]

Hi,

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

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

My question is: Did Alice fulfill Bob's demand? Are Bob going to accept Bob's qubits..?

 

[jimgraber]

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

 

[begyu85]

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... ?