Dynamics of entropic uncertainty relation under quantum channels with memory

Abstract

ABSTRACTRecently, Xu et al. [Phys. Rev. A 2012, 86, 012113] have explored the behaviour of the entropic uncertainty relation under the influence of local unital and nonunital noisy channels for a class of Bell-diagonal states. We here improve their results and investigate the entropic uncertainty relation under the influence of unital and nonunital noisy channels with memory. Different types of noisy channels with memory, such as amplitude damping channel (nonunital channel), phase-damping and depolarizing channels (unital channels) have been taken into account. Analytical or numerical results is presented. The effect of channels with memory on dynamics of the entropic uncertainty (or its lower bound) has been discussed in detail. Compare with previous results, our results show that, the entropic uncertainty (or its lower bound) subjecting to amplitude damping channel with memory will be reduced at first and then be lifted with the memory coefficient of channel μ increasing, however they will be only reduced under phase-damping and depolarizing channels in the presence of memory. Especially, in the limit of , the entropic uncertainty (or its lower bound) could be well protected and immune to decoherence of channels.