Anton Alyakin
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HF
Amplitudes and phase
A Bloch sphere beside six complex planes, one per axis state, driven by polar angle, relative phase, and a global phase.
Bloch sphere with six amplitude phasors
A Bloch sphere showing the state as a point, and six complex planes showing the amplitude of that state along each of the six axis states.
|0⟩
|1⟩
|+⟩
|−⟩
|+i⟩
|−i⟩
⟨0|ψ⟩
p = 1.00
⟨+|ψ⟩
p = 0.50
⟨+i|ψ⟩
p = 0.50
⟨1|ψ⟩
p = 0.00
⟨−|ψ⟩
p = 0.50
⟨−i|ψ⟩
p = 0.50
θ polar
0°
φ relative
0°
γ global
0°
|0⟩
|1⟩
|+⟩
|−⟩
|+i⟩
|−i⟩
spin γ
x = 0.00 y = 0.00 z = 1.00 |r| = 1.00
Spin γ.
Every dial turns. No probability moves and the sphere point holds still.
Slide φ.
The point circles a line of latitude. Only the ⟨1|ψ⟩ dial turns.
Slide θ.
The point rides a meridian.
Why twelve numbers, two knobs.
γ is a gauge choice, each column obeys p₊ + p₋ = 1, and X and Y are combinations of the Z pair.
← all three instruments