Coherent states and unilateral coherence in strengthening entropic uncertainty relations

In this paper, we examine entropy uncertainty relations in the presence of quantum memory and quantum entanglement for non-orthogonal states constructed from two-qubit coherent states. Our results reveal that for the studied state, the entropy uncertainty relations under quantum memory conditions remain tight across a broad range of parameters, leading to lower error rates and higher precision in observable predictions. We explicitly demonstrate that in the presence of quantum memory, the ability to predict observables is fundamentally tied to entanglement. Stronger entanglement leads to reduced entropy uncertainty and greater predictive accuracy. On the other hand, as entanglement weakens, even though the uncertainty relations remain tight, prediction errors increase accordingly. In the maximum entanglement state, the accuracy of the predictions is also maximized. As the entanglement decreases, despite the tightening of the uncertainty relations, the accuracy of the predictions decreases. The prediction accuracy is fully proportional to the amount of entanglement, and it is possible to achieve the desired minimum entropy uncertainty and high correlation according to the problem's requirements. This is while the numerical values of the components forming the upper bound of the entropy uncertainty relations are not equal in all cases. With respect to the changes examined from the presented state, quantum correlation, entropy uncertainty, and the components forming the upper bound, regardless of the amount of entanglement, each separately tend to a constant value.