  A measurement-induced continuous-variable logical gate is able to prepare
Schr\"odinger cat states if the gate uses a non-Gaussian resource state, such
as cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Our
scheme provides an alternative to hybrid circuits which use photon subtraction
and (or) Fock resource states and photon number detectors. We reveal the
conditions under which the gate conditionally prepares quantum superposition of
two undistorted "copies" of an arbitrary input state that occupies a finite
area in phase space. A detailed analysis of the fidelity between the gate
output state and high-quality Schr\"odinger cat state is performed. A clear
interpretation of the output state quantum statistics in terms of Wigner
function in dependence on the gate parameters and measurement outcome is
presented for a representative set of input Fock states.
