Contextual quantum metrology

We demonstrate that the contextuality of measurement selection can enhance the precision of quantum metrology with a simple linear optical experiment. Contextuality is a nonclassical property known as a resource for various quantum information processing tasks. Recent studies show that contextuality by anomalous weak values can be utilized to enhance metrological precision, unraveling the role of contextuality in quantum metrology. Our contextual quantum metrology (coQM) scheme can elevate the precision inferred from the observed Fisher information as much as six times the precision limit given by the quantum Fisher information (QFI), and, when the Godambe information is used, the precision inferred becomes about two times lower than the precision limit. We achieve the contextuality-enabled precision with two mutually complementary measurements, whereas, in the conventional method, some optimal measurements to achieve the precision limit are either theoretically challenging to find or experimentally infeasible to realize. These results highlight that the contextuality of measurement selection is applicable in practice for quantum metrology.