Abstract
We introduce a new kind of quantum states generated by repeated actions of the creation and annihilation operators on the standard nonlinear coherent states. We discuss the Klauder minimum set of conditions, which is necessary to obtain the coherent states. As an application, we consider the new quantum states to generate high amounts of entanglement, employing a beam splitter device. To detect the entanglement, we provide the conditions for obtaining the maximum-entangled and separable states, using the linear entropy as a quantifier of correlations. Therefore, we propose the possibility to obtain highly-entangled states and control the entanglement. Finally, we examine the quantum statistics of the new coherent states through the Mandel parameter and demonstrate how this quantity influences variations in the entanglement in terms of main physical parameters. The results obtained may open new prospectives in different problems of quantum information processing.