Vol.:(0123456789) Quantum Information Processing (2019) 18:148 https://doi.org/10.1007/s11128-019-2216-7 1 3 Superposition of two‑mode “Near” coherent states: non‑classicality and entanglement A. Dehghani 1  · B. Mojaveri 2  · M. Aryaie 2  · A. A. Alenabi 2 Received: 6 November 2018 / Accepted: 12 February 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, we introduce quasi-Bell states as a result of two-mode superposition of two “Near” coherent states, �, ⟩, shifted in phase by  and  2 , where the latter intro- duced by Othman et al. as a new class of quantum states attached to the simple har- monic 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, squeez- ing effect and quantum polarization. We also derive the concurrence measure to quan- tify entanglement of these states and look for conditions that provide information on which these become maximally entangled. Comparing with some cases already dis- cussed in the literature, we find that the phase angle  plays an important role in non- classical effects. We also get a connection between entanglement and the polarization degree of the introduced states. Keywords Quantum optics · Coherent states · Photon statistics · Photon counting · Squeezing · Entanglement * A. Dehghani a_dehghani@tabrizu.ac.ir; alireza.dehghani@gmail.com B. Mojaveri bmojaveri@azaruniv.ac.ir M. Aryaie m_ar1991@yahoo.com A. A. Alenabi aaalenabi7488@yahoo.com 1 Department of Physics, Payame Noor University, PO Box 19395-3697, Tehran, Islamic Republic of Iran 2 Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Islamic Republic of Iran