Quantum Entropy And Entanglement Of Vibrational States In Triatomic Molecules

The advent of quantum information science has motivated the research of quantum correlations of vibrational states in molecules.On one hand,molecular quantum computing has been theoretically exploited.On the other hand,entanglement,a seminal resource of quantum computation,has become more and more popular.Thus we are concerned with the possible relationship between quantum correlations and quantities in molecular theory.For this purpose,the dynamics of quantum entropy,energy,and entanglement is studied for various initial states in an important spectroscopic Hamiltonian of bent triatomic molecules H2O,D2O and H2S.Firstly,the total quantum correlation is quantified in terms of the mutual information and the entanglement by the concurrence borrowed from the theory of quantum information.The Pauli entropy and the intramolecular energy usually used in the theory of molecules are calculated to establish a possible relationship between both theories.A section of the two quantities among these four quantities is introduced to visualize such relationship.Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch-or bend-vibrationally localized state,the mutual information,the Pauli entropy,and the concurrence are dominant-positively correlated while they are dominantly anti-correlated with the interacting energy among three anharmonic vibrational modes.In particular,such correlation is more distinct for the localized state with high excitations in the bending mode.The nice quasi-periodicity of those quantities in molecule D2O reveals that this molecule prepared in the localized state in the stretching or the bending mode can be more appreciated for molecular quantum computation.However,the dynamical correlation of those quantities behaves irregularly for the dislocalized states.Moreover,the hierarchy of the mutual entropy and the Pauli entropy is explicitly proved.Secondly,quantum entropy and energy in every vibrational mode are investigated.Thereby,the relation between bipartite and tripartite entanglement is discussed as well.It is demonstrated that entropy and energy in the mode without or lower initial excitation are dominant-positively correlated,while both quantities in the highly excited mode are dominantly anti-positively correlated,while both quantities in the highly excited mode are dominantly anti-correlated.Bipartite and tripartite entanglement display dominantly positive correlation for the bending vibrationally localized state with high excitations.Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.In summary,we have investigated the dynamics of entropy,energy and entanglement of vibrational states in bent triatomic molecules H2O,D2O and H2S.We hope that those works can be useful in understanding the relationship between tripartite entanglement and properties in molecules,and motivates the research of quantum information in high dimensional states of molecules.