Dynamical characteristic of entropic uncertainty relation in the long-range Ising model with an arbitrary magnetic field

In this work, we explore the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) and the entanglement concurrence for the long-range Ising (LRI) model in the presence of an arbitrary magnetic field. The long-range interaction is considered as type of the Calogero-Moser interaction that is inversely proportional to the square of the distance between the spins. It is shown that the measurement's uncertainty and the entanglement concurrence are extremely sensitive to the effects of the distance between spins, the magnitude, and the direction of the external magnetic field. The evaluation of the QMA-EUR is fully related to the entanglement concurrence in case of the LRI model. At larger distances between the spins, there is inflation in the measuring uncertainty due to the fragile entanglement between them. The evolutions of the entanglement and the uncertainty show only similar dynamical characteristics in antiferromagnetic and ferromagnetic frames when the magnetic field is perpendicular to the z-axis.