  A possible way of generating nonclassical states of light, especially
non-Gaussian states, is via the truncation of a given state in the Fock basis.
In recent work, we presented an alternative scheme for such quantum scissors
[Phys. Rev. A 104, 033715 (2021)], employing a nondegenerate parametric
amplifier, a beam splitter and photodetectors. An advantage of this setup is
that it does not require the generation of Fock states beforehand, as in
previous proposals. Here we extend this treatment to mixed input states. We
show the possibilities of generating truncated states with either a maximum
Fock number N or states having a minimum Fock number N. We discuss two specific
examples of states to be truncated: i) the thermal state, and ii) the
phase-diffused coherent state. In both cases, we show that the generated states
can have significant sub-Poissonian statistics as well as non-Gaussian
character. The degree of such nonclassical properties, as well as the success
probabilities, can be changed by adjusting the parametric amplifier strength
and the beam splitter transmittance.
