Two isotropic harmonic oscillators in a magnetic field on the non-commutative phase space (NCPS) are studied in this paper.We derive the corresponding entanglement entropies of the vacuum state and we find analytically purity function, Hall conductivity and the energy density.Transition-state theory is also developed to examine the purity function and the energy density.By considering the action of the non-commutativity parameters, entanglement and Hall conductivity present a similar behavior.A large magnetic field acts as a disturbance of the accurate system information and the non-localization of the two harmonic oscillators in the atom by increasing its stored energy.The application of the transition-state theory increases entanglement and accelerates the non-localization phenomenon.