Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments

Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink’s entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.