Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

The uncertainty principle imposes constraints on an observer’s ability to make precision measurements for two incompatible observables; thus, uncertainty relations play a key role in quantum precision measurement in the field of quantum information science. Here, our aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs. Explicitly, we explore the dynamics of the uncertainty relations via entropic measures in non-Markovian regimes when two atomic qubits independently interact with their own infinite degree-of-freedom bosonic reservoir. We show that measurement uncertainty vibrates with periodically increasing amplitude with growing non-Markovianity of the observed system and ultimately saturates toward a fixed value at a long time limit. It is worth noting that there are several appealing conclusions raised by us: First, the uncertainty’s lower bound does not entirely depend on the quantum correlations within the two-qubit system, being affected by an interplay between the quantum discord and the minimal von Neumann conditional entropy \(\mathcal{S}_\mathrm{ce}\). Second, the dynamic characteristic of the measurement uncertainty is considerably distinctive with regard to Markovian and non-Markovian regimes, respectively. Third, the measurement uncertainty is closely correlated with the Bell non-locality \({\mathcal{B}}\). Moreover, we claim that the entropic uncertainty relation could be a promising tool with which to probe entanglement in current architecture.