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... ?