  The last two decades have witnessed an increasing effort of the scientific
community toward pursuing a better framework for quantum resource covariance,
with the focus predominantly posed on quantum entanglement. In this work, we
move the discussion one step further by analyzing the behavior of both genuine
multipartite entanglement and quantum coherence under Lorentz boosts.
Specifically, we conduct a case study for the problem of an electron-positron
pair created in a superposed multipartite pure state. Our approach is different
from the standard treatments also in that we consider all the components of the
four-momentum, thus allowing for an inspection of scenarios wherein
entanglement can be encoded among these degrees of freedom as well. Our
analysis reveals interesting subtleties in this problem, like the fact that
genuine 4-partite entanglement in the lab frame transforms into genuine
8-partite entanglement plus quantum coherence in the perspective of the
Lorentz-boosted frame. Moreover, a given combination of these quantum resources
is shown to form a Lorentz invariant. Although our findings are not able to
determine, via first principles, an information-theoretic Lorentz invariant,
they pave the way for fundamental incursions along this line.
