Schr\"odinger cat states prepared by logical gate with non-Gaussian resource state: effect of finite squeezing and efficiency versus monotones

TL;DR

This paper investigates how finite squeezing of a non-Gaussian resource state affects the performance of a quantum gate that produces Schrödinger cat states, revealing a saturation point in state quality improvement and questioning the applicability of certain non-Gaussianity measures.

Contribution

It provides an exact solution for the gate output state considering finite squeezing and discusses the implications for efficiency and non-Gaussianity measures in quantum gate performance.

Findings

Output cat state quality saturates with increasing squeezing.

Probability of successful measurement decreases with squeezing.

Standard non-Gaussianity measures may not reflect gate efficiency accurately.

Abstract

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.