  Quantum metrology promises higher precision measurements than classical
methods. Entanglement has been identified as one of quantum resources to
enhance metrological precision. However, generating entangled states with high
fidelity presents considerable challenges, and thus attaining metrological
enhancement through entanglement is generally difficult. Here, we show that
contextuality of measurement selection can enhance metrological precision, and
this enhancement is attainable with a simple linear optical experiment. We call
our methodology "contextual quantum metrology" (coQM). Contextuality is a
nonclassical property known as a resource for various quantum information
processing tasks. Until now, it has remained an open question whether
contextuality can be a resource for quantum metrology. We answer this question
in the affirmative by showing that the coQM can elevate precision of an optical
polarimetry by a factor of 1.4 to 6.0, much higher than the one by quantum
Fisher information, known as the limit of conventional quantum metrology. We
achieve the contextuality-enabled enhancement with two polarization
measurements which are mutually complementary, whereas, in the conventional
method, some optimal measurements to achieve the precision limit are either
theoretically difficult to find or experimentally infeasible. These results
highlight that the contextuality of measurement selection is applicable in
practice for quantum metrology.
