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Chinese Journal of Chemical Physics

Entanglement and Energy for Vibrationally Localized States in Molecule CS2

Zixin Yang, Xing Quan Shen, Xi-Wen Hou

Published Jun 1, 2015• 1 citation
Publisher

Abstract

The dynamics of quantum entanglement described by the von Neumann entropy is studied for the localized states of Fermi-resonance coupling vibrations in molecule CS2, where the interacting energy between the stretching and the bending modes is considered to establish a connection between entanglement and energy. It is shown that entanglement reveals dominant anti-correlation with the interacting energy for the stretch-localized state, while that exhibits dominantly positive correlation for the bend-localized state. The entanglement and the energy for the dislocalized states are discussed as well. Those are useful for molecular quantum computing and quantum information in high dimensional states.

DOI
10.1063/1674-0068/28/cjcp1503044

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Entanglement and Energy for Vibrationally Localized States in Molecule CS2

Zixin, Yang, Xing Xing +3 more

von Neumann 熵描述的量纠纷的动力学为在分子 CS2 联合颤动的费密回声的局部性的状态被学习，在在拉长和弯曲模式之间的交往的精力被认为建立在纠纷和精力之间的一个连接的地方。纠纷为段局部性的状态与交往的精力揭示主导的反关联，这被显示出，当那为拐弯局部性的状态展出主导地积极的关联时。为 dislocalized 状态的纠纷和精力也被讨论。那些处于高维的状态为分子的量计算和量信息是有用的。

Chinese Journal of Chemical Physics•Jan 1, 2015•0 citations
The dynamics of quantum entanglement described by the von Neumann entropy is studied for the localized states of Fermi-resonance coupling vibrations in molecule CS2, where the interacting energy between the stretching and the bending modes is considered to establish a connection between entanglement and energy. It is shown that entanglement reveals dominant anti-correlation with the interacting energy for the stretch-localized state, while that exhibits dominantly positive correlation for the bend-localized state. The entanglement and the energy for the dislocalized states are discussed as well. Those are useful for molecular quantum computing and quantum information in high dimensional states.
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.
The dynamical entanglement for Fermi coupled C-H stretch and bend vibrations in molecule CHD 3 is studied in terms of two negativities and the reduced von Neumann entropy, where initial states are taken to be direct products of photon-added coherent states on each mode. It is demonstrated that the negativity defined by the sum of negative eigenvalues of the partial transpose of density matrices is positively correlated with the von Neumann entropy. The entanglement difference between photon-added coherent states and usual coherent states is discussed as well.
The entanglement dynamics of Fermi resonance coupling vibrations in a spectroscopic Hamiltonian for molecules CHD3\mathrm{C}\mathrm{H}{\mathrm{D}}_{3}CHD3​, CHCl3\mathrm{C}\mathrm{H}{\mathrm{Cl}}_{3}CHCl3​, and CHF3\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}CHF3​ is studied in terms of the von Neumann entropy and negativity with three kinds of initial states that are direct products of coherent states, thermal states, and squeezed states of each mode. It is demonstrated that the increasing rate of entanglement in the early-time evolution is the largest for the squeezed states, while that is the smallest for the coherent states. For small parameters in the coherent and thermal states, entanglement displays a quasiperiodicity with the quasiperiod in CHF3\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}CHF3​ being the longest. Furthermore, the dynamical correlation between the von Neumann entropy and negativity shows that positively correlated or anticorrelated behaviors of both measures strongly depend on initial states and molecules. For those states with small parameters, both measures exhibit dominantly positive correlation. These are useful for molecular quantum computing and information processing.
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.
von Neumann 熵描述的量纠纷的动力学为在分子 CS2 联合颤动的费密回声的局部性的状态被学习，在在拉长和弯曲模式之间的交往的精力被认为建立在纠纷和精力之间的一个连接的地方。纠纷为段局部性的状态与交往的精力揭示主导的反关联，这被显示出，当那为拐弯局部性的状态展出主导地积极的关联时。为 dislocalized 状态的纠纷和精力也被讨论。那些处于高维的状态为分子的量计算和量信息是有用的。