Entanglement of electron pairs extracted from a many-body system

Entanglement of spins is analyzed for two electrons extracted from a mixed many-electron state by projecting onto the two-electron subspace. The concurrence formulae are expressed in a compact form for states with a well-defined square of the total spin projection. As an example, the thermal entanglement for a qubit pair with an anisotropic Heisenberg and the Dzyaloshinskii-Moriya interactions in an inhomogeneous magnetic field is given analytically. Remarkably, the concurrence of a pair of electrons with antiparallel spins and in a delocalised orbital state is given by the scalar product of the state with its spin-flipped state and not with the time-reversed state