While in classical mechanics the mean error of a measurement is solely caused by the measuring process (or device), in quantum mechanics the operator-based nature of quantum measurements has to be considered in the error measure as well. One of the major problems in quantum physics has been to generalize the classical root-mean-square error to quantum measurements to obtain an error measure satisfying both soundness (to vanish for any accurate measurements) and completeness (to vanish only for accurate measurements). A noise-operator-based error measure has been commonly used for this purpose, but it has turned out incomplete. Recently, Ozawa proposed an improved definition for a noise-operator-based error measure to be both sound and complete. Here, we present a neutron optical demonstration for the completeness of the improved error measure for both projective (or sharp) as well as generalized (or unsharp) measurements.

在经典力学中，测量的平均误差仅由测量过程（或设备）引起，而在量子力学中，在误差测量中也必须考虑量子测量的基于算子的性质。量子物理学中的主要问题之一是将经典的均方根误差推广到量子测量，以获得满足健全性（对于任何准确测量为零）和完整性（仅对于准确测量为零）的误差度量。为此目的，通常使用基于噪声运算符的误差度量，但结果证明它不完整。最近，Ozawa 提出了一种改进的基于噪声算子的误差度量的定义，该定义既合理又完整。这里，