Bloch Sphere Telemetry | 3D Geometric Representation of Qubits
Quick Technical Answer:
The Bloch sphere is a 3D unit sphere that geometrically maps any 2-level quantum state |ψ⟩ = cos(θ/2)|0⟩ + e^{iφ}sin(θ/2)|1⟩ to coordinates on or within its surface: r = (sin θ cos φ, sin θ sin φ, cos θ).
Formula / Unitary:
\vec{r} = (\langle X \rangle, \langle Y \rangle, \langle Z \rangle) = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta), \quad ||\vec{r}|| \le 1
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Frequently Asked Questions
What does a Bloch vector with length ||r|| < 1 signify?
A Bloch vector on the surface (||r|| = 1) represents a completely pure state. A vector inside the sphere (||r|| < 1) represents a mixed state experiencing decoherence, with r = 0 representing the completely maximally mixed state I/2.