Characterizing the uncertainty relation via a class of measurements

Abstract

Abstract The connection between uncertainty and entanglement is a prevalent topic in quantum information processing. Based on a broad class of informationally complete symmetric measurements, which can be viewed as a common generalization of symmetric, informationally complete positive operator-valued measures and mutually unbiased bases, a conical 2-design is calculated. This design plays a crucial role in quantum measurement theory. Subsequently, the relation between the uncertainty and the entanglement for a set of measurements is portrayed using conditional collision entropy. Furthermore, a tighter lower bound of the uncertainty relation is discussed according to the characterization of the entropic bound. Finally, the relation is applied to entanglement witnesses. It is demonstrated that the present results are unified and comprehensive.