Lorentz transformations for massive two-particle systems: entanglement change and invariant subspaces

Lorentz boosts on particles with spin and momentum degrees of freedom induce momentum-dependent rotations. Since, in general, different particles have different momenta, the transformation on the whole state is not a representation of the rotation group. Here we identify the group that acts on a two-particle system and, for the case when the momenta of the particles are correlated, find invariant subspaces that have interesting properties for quantum information processes in relativistic scenarios. A basis of states is proposed for the study of transformations of spin states under Lorentz boosts, which is a good candidate for building quantum communication protocols in relativistic scenarios.