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Explanation:
3D Quantum Visualizer6-Axis Dynamic Tracking

Interactive 3D Bloch Sphere Explorer

The Bloch Sphere provides an exact geometrical representation of 2-level quantum state space (qubit). Rotate the 3D camera to track all 6 poles, move the sliders to observe angle sweep arcs, and inspect mixed-state purity.

Qubit 0 Bloch SpherePure State
0|0\rangle(+Z)
1|1\rangle(-Z)
+|+\rangle(+X)
|-\rangle(-X)
i|i\rangle(+Y)
i|-i\rangle(-Y)
X, Y, Z(1, 0, 0)
θ\theta (Polar)90.0°
ϕ\phi (Azimuth)0.0°

Standard Basis Presets (6 Poles)

Click to snap

State Parameters

θ\theta (Polar Angle from $+Z$):90.0° (1.57 rad)
ϕ\phi (Azimuthal Angle in $XY$ plane):0.0° (0.00 rad)
P(0)=cos2(θ/2)P(|0\rangle) = \cos^2(\theta/2)50.0%
P(1)=sin2(θ/2)P(|1\rangle) = \sin^2(\theta/2)50.0%

Bloch Sphere State Vector Formulation:

ψ=cos(θ/2)0+eiϕsin(θ/2)1|\psi\rangle = \cos(\theta/2)|0\rangle + e^{i\phi}\sin(\theta/2)|1\rangle

The north pole is |0⟩, the south pole is |1⟩. Any other point on the globe is a unique quantum superposition of both, with latitude controlling probability and longitude controlling the quantum relative phase!