Entanglement, Electron Correlation, and Density Matrices

Quantifying quantum correlations in fermionic systems using witness operators

“…We start by investigating bipartite entanglement in the space A(H (4) ⊗ H (4) ), which has the smallest dimension allowing for quantum correlations in fermionic systems. In this case, we can compare the Fermionic Generalized Robustness (R F g -Eq.22) with the Schliemann concurrence (C S -Eq.9).…”

“…It is easy to see, in this simple case, that the anti-symmetrization of coordinates introduces correlations between the fermions, namely, the well known exchange contributions from the Hartree-Fock theory. On the other hand, a single Slater determinant is solution of a one-particle Schrödinger equation and, therefore, can have no quantum correlation between the particles [4]. Considering states described by more than one Slater determinant introduces additional correlations beyond the exchange contribution.…”

“…Thus, given the operator D = KU ph , called operator of dualisation, and the dual states ρ = DρD −1 , we have that the Schliemann concurrence for states ρ ∈ A(H (4) ⊗H (4) ) is given by…”

“…Fermionic systems of this kind can be described using Slater determinants [4]. Consider, for example, a two-fermion state represented by a single Slater determinant, namely,…”

“…The notion of entanglement, first noted by Einstein, Podolsky and Rosen [1], is considered one of the main features of quantum mechanics, being subject of study in several areas recently [2][3][4]. Thus, it is of paramount importance both the understanding and the quantification of entanglement in composite quantum systems, being these one of the main challenges of modern quantum theory.…”