  We present a scheme of quantum state truncation in the Fock basis (quantum
scissors), based on the combined action of a nondegenerate optical parametric
amplifier and a beamsplitter. Differently from previously proposed
linear-optics-based quantum scissors devices, which depend on reliable Fock
states sources, our scheme requires only readily available Gaussian states,
such as coherent states inputs (vacuum state included). A truncated state is
generated after performing photodetections in the global state. We find that,
depending on which output ports each of the two photodetectors is positioned,
different types of truncated states may be produced: i) states having a maximum
Fock number of $N$, or ii) states having a minimum Fock number $N$. In order to
illustrate our method, we discuss an example having as input states a coherent
state in the beamsplitter and vacuum states in the amplifier, and show that the
resulting truncated states display nonclassical properties, such as
sub-Poissonian statistics and squeezing. We quantify the nonclassicality degree
of the generated states using the Wigner-Yanase skew information measure. For
complementarity, we discuss the efficiency of the protocol, e.g., generation
probability as well as the effects of imperfections such as the detector's
quantum efficiency and dark counts rate.
