Contextual quantum metrology

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.