Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations

Abstract

In this work, we investigate the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and nonunital channels. Herein, we choose Pauli operators $\sigma _x$ and $\sigma _z$ as a pair of observables of interest measuring on particle A, and the uncertainty can be predicted when particle A is entangled with quantum memory B. We explore the dynamics of the uncertainty for the measurement under local unitary (phase-damping) and nonunitary (amplitude-damping) channels, respectively. Remarkably, we derive the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under various realistic noisy environments; it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose $\sigma _x$ and $\sigma _y$ measurement. Besides, we find out that the entropic uncertainty will have an optimal value if one chooses $\sigma _x$ and $\sigma _z$ as the measurement incompatibility, comparing with others. Furthermore, in order to reduce the entropic uncertainty in noisy environment, we propose an effective strategy to steer the amount by means of implementing a filtering operation on the particle under the two types of channels, respectively. It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength. Thus, our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.