Dynamical correlations of mutual information and tripartite entanglement for vibrational states in a trimer molecule

Abstract

Quantum mutual information and concurrence are two important measures of quantum correlations, and their similar behavior for a bipartite pure state calls for inspecting whether such a behavior remains for a multipartite pure state. The dynamical correlation of quantum mutual information and tripartite entanglement is analytically and numerically studied for initial states, total boson numbers and coupling parameters in a symmetric trimer molecule, where the entanglement is measured in terms of concurrence. A correlation parameter is introduced to describe the correlation between mutual information and concurrence. It is shown that both quantities are positively or anti-correlated in irregular manner. However, they exhibit completely positive correlation for suitable states, with their explicit expressions being presented for arbitrary model parameters. The dynamical correlation between bipartite and tripartite entanglement is discussed as well. Those shed new light on the understanding of quantum correlations of vibrational states in polyatomic molecules.