Quantum speed limit time for a two-qubit system interacting with independent and common reservoirs

We study the quantum speed limit time for a two-qubit system interacts with indepen- dent and common reservoir. The system is initially prepared in a class of X-structure density matrix, namely the extended Werner-like states (EWL). We demonstrate that when reservoir enters to the non-Markovian regime, the quantum speed limit time de- crease more sharply in a common reservoir than independent reservoirs.