  We investigate the generation of an entangled electron pair emerging from a
system composed of two quantum dots attached to a superconductor Cooper pair
beam splitter. We take into account three processes: Crossed Andreev
Reflection, cotuneling, and Coulomb interaction. Together, these processes play
crucial roles in the formation of entangled electronic states, with electrons
being in spatially separated quantum dots. By using perturbation theory, we
derive an analytical effective model that allows a simple picture of the
intricate process behind the formation of the entangled state. Several
entanglement quantifiers, including quantum mutual information, negativity, and
concurrence, are employed to validate our findings. Finally, we define and
calculate the covariance associated with the detection of two electrons, each
originating from one of the quantum dots with a specific spin value. The time
evolution of this observable follows the dynamics of all entanglement
quantifiers, thus suggesting that it can be a useful tool for mapping the
creation of entangled electrons in future applications within quantum
information protocols.
