In this paper,the output dynamics of mutually-coupled erbium-doped fiber ring lasers with time-delayed optical feedback is investigated quantitatively and discussed brie fly,in terms of an information-theory-based quantifier derived from information theory,i.e.,the permutation entropy (PE).The relationship between the quality of chaos synchronization and the chaotic comple xity is mainly focused on throughout our work.It is shown that the PE can be effectively used to detect th e dynamical changes qualitatively and quantitatively,such as steady state,peri odic state and chaotic state.Besides,the PE values calculated from the output of the mutually-coupled scheme are much higher and more stable than those for the solitary laser,which means that more complex chaotic carriers can be generated from the former system ,leading to the security enhancement of the chaotic optical communications.Moreover,we also find that, the PE values for these mutually-coupled lasers versus the embedding dimension are almost the same unde r the condition that the high-quality synchronization between them is achieved.In contrast,these PE va lues become sufficiently different when the good synchronization is not obtained,which further indicates that the PE quantifier could be employed as an effective tool to distinguish the synchronization quality between the coupled lasers,or at least capable of providing additional information on the performance of chaos synchronization.