  We show how the use of entanglement can enhance the precision of the
detection of the Unruh effect with an accelerated probe. We use the
Unruh-DeWitt model of a two-level atom interacting relativistically with a
quantum field and treat the atom as an open quantum system to derive the master
equation governing its evolution. By means of quantum state discrimination, we
detect the accelerated motion of the atom by examining its time evolving state.
It turns out that the optimal strategy for the detection of the Unruh effect,
to which the accelerated atom is sensitive, involves letting the
atom-thermometer equilibrate with the thermal bath. However, introducing
initial entanglement between the detector and an external degree of freedom
leads to an enhancement of the sensitivity of the detector. Also, the maximum
precision is attained within finite time, before equilibration takes place.
