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

In summary, Bob wants Alice to generate one million random qubits using either a complex number representation or a real 3-dimensional unit vector representation. Alice chooses to generate the unit vectors and then converts them to the complex number representation. The question is whether this transformation preserves the statistics of the random qubits. According to Jim Graber, if the goal is uniform coverage of the Bloch sphere, Bob should not be able to tell the difference and the distribution of the qubits will be uniform.
  • #1
begyu85
5
0
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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  • #2
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
 
  • #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... ?
 

1. What is a pure qubit?

A pure qubit is a two-state quantum system that can exist in a state of 0 or 1, representing the basis states of a quantum computer. It is the basic unit of quantum information and can be manipulated using quantum gates.

2. What is the significance of Alice fulfilling Bob's demand in a pure qubit question?

In a pure qubit question, Alice represents the quantum system and Bob represents the measurement or manipulation of that system. If Alice fulfills Bob's demand, it means that the quantum system has successfully undergone the desired operation or measurement.

3. How is a pure qubit different from a classical bit?

A classical bit can only exist in one of two states, 0 or 1, while a pure qubit can exist in a superposition of both states. This means that a pure qubit can represent more information and perform more complex calculations than a classical bit.

4. What is the role of entanglement in a pure qubit question?

Entanglement is a phenomenon in which two or more qubits become correlated in such a way that the state of one qubit cannot be described without also describing the state of the other qubit. In a pure qubit question, entanglement can be used to manipulate the states of multiple qubits at the same time, allowing for more efficient quantum operations.

5. How is the measurement of a pure qubit different from a classical bit?

The measurement of a pure qubit can result in a probabilistic outcome, while the measurement of a classical bit will always result in a definite outcome. This is due to the superposition of states in a pure qubit, which can only be fully determined upon measurement.

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