Effect of Environmental Temperature on the Lower Bound of the Entropic Uncertainty Relation in the Presence of Quantum Memory

Because realistic quantum systems inevitably interact with their surroundings, understanding how environmental factors affect the entropic uncertainty relation remains a major challenge. In this work, we analyze how ambient temperature impacts the lower bound of the memory-assisted entropic uncertainty relation. We model the coupling between the system and its thermal environment using a generalized amplitude damping channel, featuring temperature-dependent parameters. Notably, we find that the uncertainty lower bound drops when the damping parameter (r) decreases, and rises when it increases. By contrast, shifting the parameter) p (yields much smaller variations. This stark difference highlights our main novel finding: in a finite-temperature environment, the lower bound of the entropic uncertainty relation is significantly more sensitive to the damping parameter (r) than to (p). Ultimately, these results offer a clearer look at how thermal reservoirs influence open quantum systems and affect practical quantum information processing.