I am relatively new to the Quantum Computing world and was wondering if representing a 3 qubit system using 3 Bloch Spheres feasible and if so what would the correct way to do it?
I understand a Bloch sphere can represent a single qubit.
$$\phi = \alpha |0> + \beta |1>$$ (i.e the $|0> + |1>$ states along with it's amplitudes)
In a 2- qubit system you could represent it using two bloch spheres.
$$\phi = \alpha_1 |00> + \beta_1 |01> + \alpha_2 |10> + \beta_2 |11>$$
So one sphere for the $|00>$ and $|01>$ amplitudes and another sphere for the $|10>$ and $|11>$ amplitudes
But I am a little confused about a 3-qubit system as from what I can gather it is represented by a structure like this (granted I realise different textbooks have different notation for the amplitudes):
$$/phi = \alpha_1 |000> + \beta_1 |001> + \gamma_1 |010> + \delta_1 |011> + \alpha_2 |100> + \beta_2 |101> + \gamma_2|110> + \delta_2|111>$$
How would one divide the amplitudes with their computational basis states in order to represent phi as what I expect should be 3 Bloch spheres (as it is a 3 qubit system) Since Bloch spheres represent a single $|0>+|1>$ ? Or should there be more Bloch spheres?
For example should it actually be represented by 4 Bloch spheres in the manner: $sphere1 = \alpha_1 |000> + \beta_1 |001>$
$sphere2 = \alpha_1 |000> + \beta_1 |001>$
$sphere3 = \alpha_2 |100> + \beta_2 |101>$
$sphere4= \gamma_2|110> + \delta_2|111>$
and if this is the correct manner to represent, why is that?
Apologies if this is a silly questions, I am still very much a beginner in this field!