Quantum Decoherence via Environment Coupling

Bloch vector shrinks as qubit entangles with environment — quantum → classical

ρ(t) = e^{-γt} ρ_off + diag mix
Decoherence time τ_D = 1/γ
Off-diagonal: ρ₀₁(t) = ρ₀₁(0)e^{−γt}
Bloch vector length → 0 as t→∞