At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoires of temperatures $T_C≤ T_H$ can overperform the ideal Carnot engine: $〈 W 〉 / 〈 Q_H 〉 ≤ 1-T_C/T_H$. This inequality follows from an exact fluctuation relation involving the nonequilibrium work $W$ and heat exchanged with the hot bath $Q_H$. In a previous work [Sinitsyn N A, J. Phys. A: Math. Theor. {\bf 44} (2011) 405001] this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. Here we provide the general quantum derivation, and also extend it to the case of refrigerators, in which case Carnot's statement reads: $〈 Q_C 〉 / |〈 W 〉| ≤ (T_H/T_C-1)^{-1}$. ; Comment: 6 pages, 1 figure. Wrong signs amended in v2