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.
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