  Quantifying nonclassicality of a bosonic mode is an important but challenge
task in quantum optics. Recently, the first nonclassicality measure based on
the concept of operational resource theory has been proposed [Phys. Rev.
Research 2, 023400 (2020)], which shows several crucial properties as a
resource for quantum metrology. Here we apply the measure to evaluate and
categorize different classes of nonclassical states. We discover a class of
states that can achieve the maximum nonclassicality in the asymptotic limit of
large mean number of excitations. These states can provide the same sensitivity
in place of a squeezed vacuum in a sensing scheme, e.g., the LIGO experiments.
We also discover that the nonclassicality of certain states can be greatly
improved with a single-photon addition. Besides, we explore some examples on
how to evaluate analytically the nonclassicality of mixed states, which are in
general difficult to calculate due to the convex roof nature of the measure.
Our results will be useful for preparing and utilizing nonclassical states for
applications in precision sensing tasks, such as quadrature sensing and phase
sensing in a Mach-Zehnder interferometer.
