Some properties of coherent states with singular complex matrix argument

In the paper our aim was to study the properties of a new version of coherent states whose argument is a linear combination of two special singular square 2 x 2 matrix, having a single nonzero element, equal to 1, and two labeling complex variables as developing coefficients. We have shown that this new version of coherent states satisfies all the conditions imposed on coherent states, both of pure, as well as the mixed (thermal) states characterized by the density operator. As applications, we examined the connection between these coherent states and the notions of qubits and von Neuman entropy.