Abstract
We construct the photon-added deformed Barut-Girardello coherent states (PA-DBGCSs) for bosonic fields by discussing the Klauder minimal set of conditions required to obtain coherent states. Using this set of deformed states, we propose a useful way to generate and control the entanglement generated via unitary beam splitters for different field amplitudes Z, deformation q, and excitation number m. Therefore, we provide the possibility to create highly entangled states. Moreover, we obtain the condition for maximum and separable output beam state. Finally, we examine the statistical properties of PA-DBGCSs, in view of the Mandel parameter, and exploit a connection between this quantity and variations in the behavior of the output-state entanglement. Our result can open new prospectives in different tasks of quantum information processing.