Physical Entanglement Between Localized Orbitals

Abstract

In [arXiv:2207.03377] the first closed formula of a faithful entanglement measure applicable to realistic electron systems has been derived. In the present work, we build on this key achievement with the ultimate goal of guiding the development of quantum technologies. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This clearly demonstrates the necessity of both the reference to localized few-orbital subsystems and the implementation of the number-parity superselection rule. Accordingly, in virtue of Wick's theorem, we then provide a fully analytical study of the true physical entanglement between sites in free electron chains. In that sense, we break the common paradigm of restricting such analytical analyses to unitarily invariant settings, i.e. bipartitions of the chain into rather impractical, macroscopically large subsystems. We then upgrade this model to a hydrogen ring of interacting electrons and construct the sought-after localized orbitals. For both systems, we confirm the presence of long-distance entanglement, provided the filling fractions are sufficiently low/high.

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References in corpus (26)

• Experimental quantum teleportation
• Quantum cryptography: Public key distribution and coin tossing
• Sudden Death of Entanglement
• A complete family of separability criteria
• Optical ferris wheel for ultracold atoms
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Entanglement Measures for Single- and Multi-Reference Correlation Effects
• The entanglement entropy of one-dimensional gases
• Entanglement in fermionic systems
• Entanglement constrained by superselection rules
• Entanglement in indistinguishable particle systems
• Concept of orbital entanglement and correlation in quantum chemistry
• Investigation of metal-insulator like transition through the ab initio density matrix renormalization group approach
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Quantum Many-body Theory from a Solution of the $N$-representability Problem
• Quantum correlations in molecules: from quantum resourcing to chemical bonding
• Two-orbital quantum discord in fermion systems
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond
• Teleporting quantum information encoded in fermionic modes
• Quantum teleportation of single-electron states
• Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians
• Classical and Quantum Orbital Correlations in the Molecular Electronic States
• Quantifying Electron Entanglement Faithfully
• Orbital and electronic entanglement in quantum teleportation schemes
• Comment on 'Reasonable fermionic quantum information theories require relativity'

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• Spin-free orbital entropy, mutual information, and correlation analysis
• Degrees of Entanglement in Systems of Three Indistinguishable Bosons: Revisiting the Greenberger-Horne-Zeilinge State
• Statistics of Marginal Wavefunctions as a Real-Space Diagnostic of Quantum Entanglement