Quantum-memory-assisted entropic uncertainty in fluctuating electromagnetic field with a boundary

In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation for a two-level atom coupled with fluctuating electromagnetic field in the presence of a perfectly reflecting plane boundary. The solution of the master equation that governs the system evolution is derived. We find that entropic uncertainty and mixedness increase to a stable value with evolution time, but quantum correlation reduces to zero with evolution time. That is, the mixedness is positively associated with entropic uncertainty, however, increasing quantum correlation can cause the decrease of the uncertainty. The tightness of entropic uncertainty grows at first and then declines to zero with evolution time. In addition, entropic uncertainty fluctuates to relatively stable values with increasing the atom’s distance from the boundary, especially for short evolution time, which suggests a possible way of testing the vacuum fluctuating and boundary effect. Finally, we propose an effective method to control the uncertainty via quantum weak measurement reversal.