Physical entanglement between localized orbitals

Abstract The goal of the present work is to guide the development of quantum technologies in the context of fermionic systems. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This demonstrates the significance of the number-parity superselection rule and highlights the relevance of localized few-orbital subsystems for quantum information processing tasks. Then, we explore and quantify the entanglement between localized orbitals in two systems, a tight-binding model of non-interacting electrons and the hydrogen ring. For this, we apply the first closed formula of a faithful entanglement measure, derived in (arXiv: 2207.03377 ) as an extension of the von Neumann entropy to genuinely correlated many-orbital systems. For both systems, long-distance entanglement is found at low and high densities η , whereas for medium densities, η ≈ 1 2 , practically only neighboring orbitals are entangled. The Coulomb interaction does not change the entanglement pattern qualitatively except for low and high densities where the entanglement increases as function of the distance between both orbitals.