Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments

The dynamic properties of the quantum-memory-assisted entropic uncertainty relation for a system comprised of a qubit to bemeasured and a memory qubit are investigated. We explore the behaviors of the entropic uncertainty and its lower bound in three different cases: Only one of the two qubits interacts with an external environment and subjects to quantum-jump-based feedback control, or both of the two qubits independently experience their own environments and local quantum-jump-based feedback control. Our results reveal that the quantum-jump-based feedback control with an appropriate feedback parameter can reduce the entropic uncertainty and its lower bound, and for the three different scenarios, the reduction in the uncertainty relates to different physical quantities. Besides, we find out that the quantum-jumpbased feedback control not only can remarkably decrease the entropic uncertainty, but also can make the uncertainty reach its lower bound where the dynamical map becomes unital.