Schrödinger cat states prepared by logical gate with non-Gaussian resource state: Effect of finite squeezing and efficiency versus monotones

Abstract

Quantum measurement-induced gate based on entanglement with ideal cubic phase state used as a non-Gaussian resource is able to produce Shrödinger cat state in the form of two high fidelity “copies” of the target state on the phase plane (Masalaeva and Sokolov, 2022 [21]). In this work we examine the effect of finite initial squeezing of the resource state on the gate performance. We present an 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 improve 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 negativity and non-Gaussianity, may not be directly applicable to assess the efficiency of non-Gaussian gates, which are based on quantum entanglement and subsequent projective measurement.