  Quantum measurement-induced gate based on entanglement with ideal cubic phase
state used as a non-Gaussian resource is able to produce Shr\"odinger cat state
in the form of two high fidelity ``copies'' of the target state on phase plane
[N.I. Masalaeva, I.V. Sokolov, Phys. Lett. A 424, 127846 (2022)]. In this work
we examine the effect of finite initial squeezing of the resource state on the
gate performance. We present exact solution for the gate output state and
demonstrate that there exists a degree of squeezing, available in experiment,
such that the output cat state quality almost does not impove with the further
increase of squeezing. On the other hand, the probability of the expected
ancilla measurement outcome decreases with squeezing. Since an overall
efficiency of the conditional scheme should account for the probability of
success, we argue that such measures of non-Gaussianity of the resource state
as Wigner logarithmic negativiy and non-Gaussianity may not be directly
applicable to assess the efficiency of non-Gaussian gates based on quantum
entanglement and subsequent projective measurement.
