Tight thermodynamic uncertainty relation for quantum machines

For a time-integrated current $J$ in a nonequilibrium steady state with total entropy production $\Sigma$ ($k_B = 1$), classical Markov dynamics obey $\operatorname{Var}(J) / \langle J\rangle^2 \ge 2 / \Sigma$. For quantum steady states (Lindblad dynamics, coherent transport), determine the tightest universal lower bound on $\operatorname{Var}(J) / \langle J\rangle^2$ as a function of $\Sigma$ and of system data such as Hilbert-space dimension $d$ or dynamical activity.

A proved bound together with an explicit model that saturates it.