LAUSR

Abstract We investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under two typical categories of noise: phase damping channel and amplitude damping channel. It is shown that, the entropic uncertainty monotonically increases and tends to a steady-state value with the increase of decoherence in phase damping channel, and can always keep its lower bound during the evolution when the initial state is the maximum entangled state. In contrast, under the amplitude damping channel with memory, the entropic uncertainty always fails to reach its lower bound, even in the decoherence-free subspace formed by it. Besides, the entropic uncertainty and its lower bound firstly increase with time, then turn down and tend to steady-state values. Our investigations might offer an insight into the dynamics of the measurement uncertainty under decoherence, and are important to quantum precision measurement in open systems.