t = 0
⟨σ_x⟩ = —
⟨σ_y⟩ = —
⟨σ_z⟩ = —
|Bloch| = —
Purity Tr(ρ²) = —
⟨σ_x⟩ = —
⟨σ_y⟩ = —
⟨σ_z⟩ = —
|Bloch| = —
Purity Tr(ρ²) = —
T₁ = 1/γ₁ (relax)
T₂ = 1/(γ₁/2+γ_φ) (decohere)
T₂ ≤ 2T₁
The Lindblad equation dρ/dt = −i[H,ρ] + Σ_k γ_k(L_k ρ L_k† − ½{L_k†L_k,ρ}) governs open quantum systems. For a qubit, it describes decoherence (loss of phase) and relaxation (energy decay) as the Bloch vector spirals toward the equilibrium point.