Soundness and completeness of quantum root-mean-square errors

By Masanao Ozawa. npj Quantum Information, 2018

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Defining and measuring the error of a measurement is one of the most fundamental activities in experimental science. However, quantum theory shows a peculiar difficulty in extending the classical notion of root-mean-square (rms) error to quantum measurements. A straightforward generalization based on the noise-operator was used to reformulate Heisenberg’s uncertainty relation on the accuracy of simultaneous measurements to be universally valid and made the conventional formulation testable to observe its violation. Recently, its reliability was examined based on an anomaly that the error vanishes for some inaccurate measurements, in which the meter does not commute with the measured observable. Here, we propose an improved definition for a quantum generalization of the classical rms error, which is state-dependent, operationally definable, and perfectly characterizes accurate measurements. Moreover, it is shown that the new notion maintains the previously obtained universally valid uncertainty relations and their experimental confirmations without changing their forms and interpretations, in contrast to a prevailing view that a state-dependent formulation for measurement uncertainty relation is not tenable.Quantum measurements: A classic errorAn improved definition extends the notion of root-mean-square error from classical to quantum measurements. How to define and measure the error of a measurement is one of the basic characteristics of experimental science. The root-mean-square error is a frequently used metric, but extending this notion from classical to quantum measurements is not trivial. Attempts to generalize this error to quantum measurements have been made, but many approaches suffer from anomalies, which unwantedly see the error vanish for certain types of measurements. Masanao Ozawa from Nagoya University now presents an improved definition for a quantum generalization of the classical root-mean-square error, which doesn’t suffer from such limitations.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/623b0b2f234f605149441fd21a025f12bd1a2767