  The high degree of control available over individual atoms enables precision
tests of fundamental physical concepts. In this Letter, we experimentally study
how precision measurements can be improved by preparing entangled states immune
to the dominant source of decoherence. Using \Ca ions, we explicitly
demonstrate the advantage from entanglement on a precision test of local
Lorentz invariance for the electron. Reaching the quantum projection noise
limit set by quantum mechanics, we observe for bipartite entangled states the
expected gain of a factor of two in the precision. Under specific conditions,
multipartite entangled states may yield substantial further improvements. Our
measurements improve the previous best limit for local Lorentz invariance of
the electron using \Ca ions by factor of two to four to about
$5\times10^{-19}$.
