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In this paper, we consider the preparation of Schr\"odinger cat states usinga measurement-assisted gate based on the Fock resource state, the quantumnon-demolition (QND) entangling operation, and the homodyne measurement.Previously we have investigated the gate, which for the same goal uses theancillary non-Gaussian cubic phase state generated from quadrature squeezedstates at realistic (finite) squeezing. It is of evident interest to comparethe efficiency of both schemes, that is, their ability to produce cat-likesuperpositions with high fidelity and probability of success. We introduce, inparallel with the exact theoretical description of the gate operation, a clearvisual interpretation of the output state based on the semiclassical mapping ofthe input field variables. The emergence of the superpositions of copies of theinput state in both schemes is due to the fact that such mapping is compatiblewith two (or, in general, more) sets of values of the output field observables.We demonstrate that even fine details of the output of both gates areeffectively predicted and interpreted in our approach. We examine the fidelityand success probability and reveal the ranges of physical parameters where theFock state-based and the cubic phase state-based gates demonstrate comparablefidelity and (or) probability of success.

Measurement-assisted non-Gaussian gate for Schr\"odinger cat states preparation: Fock resource state versus cubic phase state