Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

Entropy, energy, and entanglement of localized states in bent triatomic molecules

Qiang Yuan, Xi-Wen Hou

Published Feb 15, 2017• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979217500886

Related papers

Entanglement and Energy for Vibrationally Localized States in Molecule CS2

Zixin Yang, Xing Quan Shen, Xi-Wen Hou

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.

Chinese Journal of Chemical Physics•Jun 1, 2015•1 citation

Dynamics of Tripartite Entanglement and Intramolecular Energy in Symmetric Trimer Molecule

Di Yi, Xing-lin Jian, Xi-Wen Hou

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.

Chinese Journal of Chemical Physics•Apr 1, 2016•0 citations

Intramolecular energy transfer, entanglement, and decoherence in molecular systems

Liang-Jun Zhai, Yujun Zheng

The intramolecular energy transfer, dynamical entanglement of vibrations, and decoherence process in triatomic molecular systems are studied. The benchmark molecules of ${\mathrm{H}}_{2}\mathrm{S}$, ${\mathrm{NO}}_{2}$, and ${\mathrm{O}}_{3}$ are sampled to investigate the intramolecular energy transfer and dynamical entanglement of stretching-stretching vibrational modes in triatomic molecular systems by restricting the bending vibration to its ground state. The comparative study is applied to explore the dynamical differences of initial local-mode and normal-mode characteristic states. Also, the decoherence process of the stretching-stretching qubits system caused by the bending vibration is discussed.

Physical Review A•Jul 8, 2013•16 citations

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

Mo Hou, Yingqing Xia, Xi-Wen Hou

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.

International Journal of Modern Physics B•Feb 13, 2015•0 citations

Entropy correlation and entanglement for mixed states in an algebraic model

Xi-Wen Hou, Jinghua Chen, Ming-Fang Wan +1 more

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.

Journal of Physics A Mathematical and Theoretical•Jan 21, 2009•7 citations

Dynamical entanglement of vibrations in an algebraic model

Xi-Wen Hou, Jing-Hua Chen, Zhong-Qi Ma

The dynamical entanglement of two stretching vibrations of triatomic molecules ${\mathrm{H}}_{2}\mathrm{O}$ and $\mathrm{S}{\mathrm{O}}_{2}$ in an algebraic model is studied in terms of the reduced-density linear entropy with initial states that are, respectively, taken to be the product of Fock states and coherent states on each bond. It is shown that the entanglement of initial states with local-mode character is regular while that of states with normal-mode character is irregular. For initial coherent states with a small amplitude, the regularity of the entanglement with a long period appears in $\mathrm{S}{\mathrm{O}}_{2}$ and ``classical'' beat phenomena of the entanglement happens in ${\mathrm{H}}_{2}\mathrm{O}$, where the period of the beat is longer. Those long periods of the entanglement indicate that the entanglement sustains long enough so that quantum information process and quantum computation could be accomplished.

Physical Review A•Dec 28, 2006•33 citations
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 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 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.
The intramolecular energy transfer, dynamical entanglement of vibrations, and decoherence process in triatomic molecular systems are studied. The benchmark molecules of H2S{\mathrm{H}}_{2}\mathrm{S}H2​S, NO2{\mathrm{NO}}_{2}NO2​, and O3{\mathrm{O}}_{3}O3​ are sampled to investigate the intramolecular energy transfer and dynamical entanglement of stretching-stretching vibrational modes in triatomic molecular systems by restricting the bending vibration to its ground state. The comparative study is applied to explore the dynamical differences of initial local-mode and normal-mode characteristic states. Also, the decoherence process of the stretching-stretching qubits system caused by the bending vibration is discussed.
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.
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.
The dynamical entanglement of two stretching vibrations of triatomic molecules H2O{\mathrm{H}}_{2}\mathrm{O}H2​O and SO2\mathrm{S}{\mathrm{O}}_{2}SO2​ in an algebraic model is studied in terms of the reduced-density linear entropy with initial states that are, respectively, taken to be the product of Fock states and coherent states on each bond. It is shown that the entanglement of initial states with local-mode character is regular while that of states with normal-mode character is irregular. For initial coherent states with a small amplitude, the regularity of the entanglement with a long period appears in SO2\mathrm{S}{\mathrm{O}}_{2}SO2​ and ``classical'' beat phenomena of the entanglement happens in H2O{\mathrm{H}}_{2}\mathrm{O}H2​O, where the period of the beat is longer. Those long periods of the entanglement indicate that the entanglement sustains long enough so that quantum information process and quantum computation could be accomplished.