  Quantum coherence is the basic concept of superposition of quantum states and
plays an important role in quantum metrology. We show how a pair of uniformly
accelerated observers with a local two-mode Gaussian quantum state affects the
Gaussian quantum coherence. We find that the quantum coherence decreases with
increasing acceleration, which is due to the Unruh effect that destroys the
quantum resource. Essentially, the variation of quantum coherence is caused by
the modes mismatch between the input and output mode. Through 2000 randomly
generated states, we demonstrate that such mismatch is dominated by the
acceleration effect and mildly affected by the waveform parameters. Moreover,
the squeezing parameter acted as a suppressor of the reduced coherence, but it
tended to be invalid in the high squeezing. In addition, the squeezing
parameter can act as a suppressor of the reduced coherence, but the effect of
the squeezing parameter tends to be ineffective under high squeezing
conditions.
