  In this paper, we study how a displacement of a quantum system appears under
a change of relativistic reference frame. We introduce a generic method in
which a displacement operator in one reference frame can be transformed into
another reference frame. It is found that, when moving between non-inertial
reference frames there can be distortions of phase information, modal structure
and amplitude. We analyse how these effects affect traditional homodyne
detection techniques. We then develop an in principle homodyne detection scheme
which is robust to these effect, called the ideal homodyne detection scheme. We
then numerically compare traditional homodyne detection with this in principle
method and illustrate regimes when the traditional homodyne detection schemes
fail to extract full quantum information.
