  Quantum properties of vector boson scattering $V'_1V'_2\to V_1 V_2$, related
to entanglement and violation of Bell inequalities, are explored in this paper.
The analysis is based on the construction of the polarization density matrix
associated to the final state $V_1V_2$ by means of the computation of the
corresponding tree level amplitudes within the Standard Model. The aim of this
work is to determine the regions of the phase space where the final vector
bosons after the scattering result entangled and if is it possible to test the
Bell inequalities in those regions. We found that in all cases the entanglement
is present. The amount of it depends on the process and the Maximally Entangled
state is reached in some particular channels. Concerning the Bell inequality,
it could be also tested in certain kinematical regions for some of these
processes. This work is a first step in the analysis of these quantum
properties for this kind of processes and it is postponed for future studies
the reconstruction of the polarization density matrix and the related quantum
parameters from experimental data through Monte-Carlo simulations using quantum
tomography techniques.
