Lindblad Master Equation — Open Quantum Decay

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.

t = 0
⟨σ_x⟩ =
⟨σ_y⟩ =
⟨σ_z⟩ =
|Bloch| =
Purity Tr(ρ²) =
T₁ = 1/γ₁ (relax) T₂ = 1/(γ₁/2+γ_φ) (decohere) T₂ ≤ 2T₁