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Interactive 3D Bloch Sphere Explorer

Qubit 0Pure State
∣0⟩|0\rangle(+Z)
∣1⟩|1\rangle(-Z)
∣+⟩|+\rangle(+X)ACTIVE
∣−⟩|-\rangle(-X)
∣i⟩|i\rangle(+Y)
∣−i⟩|-i\rangle(-Y)
θ:90.0°
X, Y, Z(1, 0, 0)
θ\theta (Polar)90.0°
ϕ\phi (Azimuth)0.0°

Standard Basis Presets (6 Poles)

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State Parameters

θ\theta (Polar):90.0°
ϕ\phi (Phase):0.0°
P(∣0⟩)=cos⁡2(θ/2)P(|0\rangle) = \cos^2(\theta/2)50.0%
P(∣1⟩)=sin⁡2(θ/2)P(|1\rangle) = \sin^2(\theta/2)50.0%
State Formulation
∣ψ⟩=cos⁡(θ2)∣0⟩+eiϕsin⁡(θ2)∣1⟩|\psi\rangle = \cos(\frac{\theta}{2})|0\rangle + e^{i\phi}\sin(\frac{\theta}{2})|1\rangle

Latitude controls probability; longitude controls the quantum relative phase.

Qiskit Statevector
psi = Statevector([np.cos(1.57/2), np.exp(1j*0.00)*np.sin(1.57/2)])
bloch = [1.00, 0.00, 0.00]