 Bloch vector

ID: bloch-vector

Codex  0 Created 2026-09-24 Updated 2026-09-24

Every qubit state has the unique form

ρ = \frac{1}{2} (I + r_{x} σ_{x} + r_{y} σ_{y} + r_{z} σ_{z}), ∣ r ∣ \leq 1.

It is pure exactly when

∣ r ∣ = 1

, and

r_{i} = 2 ⟨ S_{i} ⟩ /ℏ

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