  In the present work, we study the interplay between relativistic effects and
quantumness in the system of two relativistic fermions. In particular, we
explore entropic measures of quantum correlations and quantum discord before
and after application of a boost and subsequent Wigner rotation. We also study
the positive operator-valued measurements (POVM) invasiveness before and after
the boosts. While the relativistic principle is universal and requires Lorentz
invariance of quantum correlations in the entire system, we have found specific
partitions where quantum correlations stored in particular subsystems are not
invariant. We calculate quantum discords corresponding of the states before and
after applying a boost, and observe that the state gains extra discord after
the boost. When analyzing the invasiveness of the POVMs, we have found that the
POVM applied to the initial entangled state reduces the discord to zero.
However, discord of the boosted state survives after the same POVM. Thus we
conclude that the quantum discord generated by Lorentz boost is robust
concerning the protective POVM, while the measurement exerts an invasive effect
on the discord of the initial state. Finally, we discuss potential
implementation of the ideas of this work using top quarks as a benchmark
scenario.
