Entropic Uncertainty Relation Under Dissipative Environments and Its Steering by Local Non-unitary Operations

Abstract

Entropic uncertainty relation (EUR) quantifies the precision of measurements for arbitrary two non-commuting observables within a specified system. Due to exposure in a noisy environment, a practical system unavoidably suffers from decay by interacting with the environment. Inthis paper, we investigate the dynamic behaviors of EUR for a pair of non-commuting observables under two typical dissipative environments. Specifically, we study the dynamics features of EUR in a single-qubit system under the degradation induced by amplitude damping (AD) and depolarizing noises, respectively. It has been found that AD and depolarizing noises do not always cause the increase of the uncertainty, and can reduce the amount in a relative long-time regime. Remarkably, it has been shown that there exists a critical phenomenon that AD noise can always lead to the reducing of the uncertainty when the ratio of ground state and excited state is beyond a threshold in the system. Furthermore, we propose a general and effective approach to steer EUR by means of a kind of non-unitary operations, namely, quantum weak measurements. It is verified that quantum weak measurements can effectively reduce the entropic uncertainty in the dissipative environment.