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International Journal of Modern Physics B

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

Mo Hou, Yingqing Xia, Xi-Wen Hou

Published Feb 13, 2015• 0 citations
Publisher

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.

DOI
10.1142/s0217979215500630

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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.
The dynamics of tripartite entanglement and intramolecular energy for one harmonic- and two anharmonic-vibrational modes in a symmetric trimer molecule is studied for various initial states, where the entanglement is quantified in terms of concurrence and the interacting energy among three modes is calculated to establish a link between entanglement and energy. It is shown that the concurrence and the interacting energy behave dominantly positive correlation for the localized state in the anharmonic-vibrational mode, while they are dominantly anti-correlated for the localized state in the harmonic-vibrational mode. The relation between bipartite entanglement and the energy in a subsystem is discussed as well. Those are useful for quantum computing and quantum information in high dimensional states prepared in polyatomic molecules.
In the present study, the dynamical behaviors of tripartite entanglement of vibrations in triatomic molecules are studied based on the Lie algebraic models of molecules. The dynamical behaviors of tripartite entanglement of the local mode molecule H2O and normal mode molecule NO2 are comparatively studied for different initial states by employing the general concurrence. Our results show that the dynamics of tripartite entanglement are relied on the dynamics of intramolecular energy distribution. The local mode molecule is more suitable to construct the tripartite entangled states. Also, the greater degree of tripartite entanglement can be obtained if the stretching vibration is first excited. These results shed new light on the understanding of quantum multipartite entanglement of vibrations in the polyatomic molecules.
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. 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. Sections of two quantities among these four quantities are introduced to visualize such relationship. Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch- or the 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 D2O molecule 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 correlations of those quantities behave irregularly for the dislocalized states. Moreover, the hierarchy of the mutual information and the Pauli entropy is explicitly proved. Quantum entropy and energy in every vibrational mode are investigated. Thereby, the relation between bipartite and tripartite entanglements is discussed as well. Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing.
Abstract We investigate a two-qubit system to understand the relationship between concurrence and mutual information, where the former determines the amount of quantum entanglement, whereas the latter is its classical residue after performing local projective measurement. For a given ensemble of random pure states, in which the values of concurrence are uniformly distributed, we calculate the joint probability of concurrence and mutual information. Although zero mutual information is the most probable in the uniform ensemble, we find positive correlation between the classical information and concurrence. This result suggests that destructive measurement of classical information can be used to assess the amount of quantum information.
For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.