The quantum speed limit time τ_QSL (black-solid line) and the trace distance D(ρ_τ,ρ_{τ + τD}) (blue-dotted line) as functions of the initial time parameter τ for a mixed initial state. (a) Δ = 0.6; (b) Δ = 0.9; (c) Δ = 1; (d) Δ = − 1. Other parameters are τ_D = 1 and p = 0.6.