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A measurement-induced continuous-variable logical gate is able to prepareSchr\"odinger cat states if the gate uses a non-Gaussian resource state, suchas cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Ourscheme provides an alternative to hybrid circuits which use photon subtractionand (or) Fock resource states and photon number detectors. We reveal theconditions under which the gate conditionally prepares quantum superposition oftwo undistorted "copies" of an arbitrary input state that occupies a finitearea in phase space. A detailed analysis of the fidelity between the gateoutput state and high-quality Schr\"odinger cat state is performed. A clearinterpretation of the output state quantum statistics in terms of Wignerfunction in dependence on the gate parameters and measurement outcome ispresented for a representative set of input Fock states.

Quantum statistics of Schr\"odinger cat states prepared by logical gate with non-Gaussian resource state