Superposition of two-mode "Near" coherent states: non-classicality and entanglement

In this paper, we introduce quasi-Bell states as a result of two-mode superposition of two "Near" coherent states, $|\alpha ,\delta \theta ⟩$, shifted in phase by $\pi$ and $\frac{\pi }{2}$, where the latter introduced by Othman et al. as a new class of quantum states attached to the simple harmonic oscillator which generated via a Mach–Zehnder interferometer. To gain insight into useful attributes to quantum information theory, we present a general analysis of non-classical properties such as photon counting probability, photon statistics, squeezing effect and quantum polarization. We also derive the concurrence measure to quantify entanglement of these states and look for conditions that provide information on which these become maximally entangled. Comparing with some cases already discussed in the literature, we find that the phase angle $\delta \theta$ plays an important role in non-classical effects. We also get a connection between entanglement and the polarization degree of the introduced states.