Quantum statistics of Schrodinger cat states prepared by logical gate with non-Gaussian resource state

A measurement-induced continuous-variable logical gate is able to prepare Schrodinger 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 Schrodinger 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.