Local quantum uncertainty and non-commutativity measure discord in two-mode photon-added entangled coherent states

In this paper, we investigate quantum correlations in entangled coherent states with photon added, which are produced by the creation operator acting on Bell-like entangled coherent states. The non-classical characteristics of the quantum state created by combining two-mode coherent states with any number of photons added are also taken into account. We provide explicit expressions for the pairwise quantum correlations found in superpositions of coherent states with m,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( m,n\right)$$\end{document}-photon addition. A comparison study between a non-commutativity discord-like measure and the evaluation of the local quantum uncertainty to measure quantum correlations is also produced. We consider some special superpositions of Bell-like entangled coherent photon-added states to be illustrative of our analytical findings. The amount of entangled even/odd coherent states of two modes coherent states with a number of photon added by non-commutativity discord is found that to be more entangled than the local quantum uncertainty. Finally, the non-commutativity discord and local quantum uncertainty under a dephasing channel is discussed.