Quantum Entanglement of Photon-Added Coherent States on a Beam Splitter

The study of new quantum states and methods for their generation is an important part of the current development of quantum technologies. One of the most important characteristics of such states is their quantum entanglement. Photon-added coherent states, which are defined as \({\text{|}}\alpha ,n\rangle = {{\mathcal{N}}_{n}}{{({{\hat {a}}^{\dag }})}^{n}}{\text{|}}\alpha \rangle \), where \({{\mathcal{N}}_{n}}\) is the normalization constant, \({\text{|}}\alpha \rangle \) is the coherent state, \({{\hat {a}}^{\dag }}\) is the creation operator, and n is the number of added photons, have been introduced relatively recently. The quantum entanglement of such states passing through a beam splitter has been considered for the first time in this work. A simple analytical representation of the wavefunction at the outputs of the beam splitter has been found and the quantum entanglement of the resulting two-qubit states has been considered. It has been shown that new quantum states have good prospects for their use in quantum technologies.