Controlling the quantum speed limit time for unital maps via filtering operations

The minimum time a system needs to change from an initial state to a final orthogonal state is called quantum speed limit time. Quantum speed limit time can be used to quantify the speed of the quantum evolution. The speed of the quantum evolution will increase, if the quantum speed limit time decreases. In this work we will use relative purity based bound for quantum speed limit time. It is applicable for any arbitrary initial state. Here, we investigate the effects of filtering operation on quantum speed limit time. It will be observed that for some intervals of filtering operation parameter the quantum speed limit time is decreased by increasing filtering operation parameter and for some other intervals it is decreased by decreasing filtering operation parameter.