Lindblad master equation · T₁/T₂ relaxation · amplitude damping vs pure dephasing
The Bloch sphere represents a qubit state: ρ = (I + r⃗·σ⃗)/2. Under the Lindblad master equation, the Bloch vector decays: dBz/dt = −(Bz+1)/T₁ (energy relaxation toward ground state), dBx/dt = −Bx/T₂, dBy/dt = ωBz − By/T₂. T₂ ≤ 2T₁ always. Pure dephasing τ_φ: 1/T₂ = 1/(2T₁) + 1/τ_φ. The trajectory spirals inward on the sphere from the initial state (θ₀, φ₀) toward |0⟩.