Improving entropic uncertainty lower bound using weak measurement and measurement reversal

The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is expressed in terms of the entropic measures. ‎In this work‎, ‎we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory‎. ‎Alice measures on her particle A and Bob‎, ‎with memory particle B, ‎predicts the Alice s measurement outcomes‎. ‎This approach has a wide range of applications such as ‎entanglement witnessing and quantum key distribution‎. ‎We study the effects of the environment on the entropic uncertainty lower bound at the presence of weak measurement and measurement reversal‎. ‎The dynamical model presented in this work is as follows‎: ‎first the weak measurement is performed‎, ‎then the decoherence affects the system and finally the measurement reversal is performed on the quantum system‎. ‎Here, we consider the generalized amplitude damping channel as environmental noise‎. ‎We will show that at the presence of weak measurement and measurement reversal‎, ‎despite the presence of environmental factors‎, ‎the entropic uncertainty lower bound drops to an optimal minimum value‎. ‎In fact‎, ‎weak measurement and measurement reversal enhance the quantum correlation between the subsystems A and B, and thus the uncertainty of Bob regarding Alice s measurement outcomes reduces.