  We investigate how relativistic acceleration of the observers can affect the
performance of the quantum teleportation and dense coding for continuous
variable states of localized wavepackets. Such protocols are typically
optimized for symmetric resources prepared in an inertial frame of reference. A
mismatch of the sender's and the receiver's accelerations can introduce
asymmetry to the shared entanglement, which has an effect on the efficiency of
the protocol that goes beyond entanglement degradation due to acceleration. We
show how these asymmetry losses can be reduced by an extra LOCC step in the
protocols.
