Correlation paradox of the dissociation limit: A quantum information perspective

Abstract

The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule: While a significant increase of the distance $r$ between the two nuclei marginalizes the electron-electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature $T$ will destroy the entanglement beyond a critical separation distance $r_{\mathrm{crit}}$($T$) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.

arXiv commenttitle has been modified, close to published version

References in corpus (51)

• Quantum entanglement
• Experimental quantum teleportation
• Concentrating Partial Entanglement by Local Operations
• Entanglement in quantum critical phenomena
• Entanglement detection
• Quantifying Entanglement
• Entanglement in a simple quantum phase transition
• Quantum Resource Theories
• The Role of Relative Entropy in Quantum Information Theory
• Entanglement renormalization
• Sudden Death of Entanglement
• Quantum Cryptography with Entangled Photons
• Entanglement monotones
• Area laws in quantum systems: mutual information and correlations
• On the role of entanglement in quantum computational speed-up
• Entanglement Measures under Symmetry
• Thermodynamics and the Measure of Entanglement
• Entanglement and quantum phase transition in the extended Hubbard model
• Local entanglement and quantum phase transition in the Hubbard model
• Quantum Correlations in Two-Fermion Systems
• The entanglement of indistinguishable particles shared between two parties
• Virtual Quantum Subsystems
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Fractional spins and static correlation error in density functional theory
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Entanglement Measures for Single- and Multi-Reference Correlation Effects
• Entanglement in fermionic systems
• Fermionic mode entanglement in quantum information
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Orbital entanglement in bond-formation processes
• Experimental Implementaton of Dense Coding Using Nuclear Magnetic Resonance
• Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations
• Orbital entanglement in quantum chemistry
• Entanglement constrained by superselection rules
• Nonlocal resources in the presence of Superselection Rules
• Quantum nonlocality in the presence of superselection rules and data hiding protocols
• Entanglement, quantum phase transitions, and density matrix renormalization
• Reasonable fermionic quantum information theories require relativity
• New measure of electron correlation
• The correlation theory of the chemical bond
• A Dynamic Systems Approach to Fermions and Their Relation to Spins
• Imaging of atomic orbitals with the Atomic Force Microscope - experiments and simulations
• Particle partitioning entanglement in itinerant many-particle systems
• Spectral properties of reduced fermionic density operators and parity superselection rule
• Optimal free descriptions of many-body theories
• Information geometry of density matrices and state estimation
• Quantum Marginal Problem and its Physical Relevance
• Free-fermion descriptions of parafermion chains and string-net models
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Correlation in fermion or boson systems as the minimum of entropy relative to all free states
• Nonfreeness and related functionals for measuring correlation in many-fermion states

Cited by in corpus (30)

• Entanglement in indistinguishable particle systems
• Pythonic Black-box Electronic Structure Tool (PyBEST). An open-source Python platform for electronic structure calculations at the interface between chemistry and physics
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Fermionic systems for quantum information people
• Orbital entanglement and correlation from pCCD-tailored Coupled Cluster wave functions
• Quantum correlations in molecules: from quantum resourcing to chemical bonding
• Quantum Information-Assisted Complete Active Space Optimization (QICAS)
• Two-orbital quantum discord in fermion systems
• Quantum Proton Effects from Density Matrix Renormalization Group Calculations
• One-body entanglement as a quantum resource in fermionic systems
• The relationship between structure and excited-state properties in polyanilines from geminal-based methods
• Bootstrap Embedding on a Quantum Computer
• Physical Entanglement Between Localized Orbitals
• Many-body entanglement in fermion systems
• Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality
• Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians
• Hydrogenic entanglement
• Delving into the Catalytic Mechanism of Molybdenum Cofactors: A Novel Coupled Cluster Study
• Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals
• Entanglement and non-locality in quantum protocols with identical particles
• Locality and entanglement of indistinguishable particles
• Orbital Entanglement and The Double $d$-Shell Effect in Binary Transition Metal Molecules
• Mode Entanglement in Fermionic and Bosonic Harmonium
• Entanglement of particles versus entanglement of fields: independent quantum resources
• Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
• Spin-free orbital entropy, mutual information, and correlation analysis
• Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer
• A Quantum Information Perspective on Many-Body Dispersive Forces
• Geometric Constraints on Two-electron Reduced Density Matrices
• Analysis of quantum correlations within the ground state of a three level Lipkin model