Quantum statistics of Schr\"odinger cat states prepared by logical gate with non-Gaussian resource state

TL;DR

This paper proposes a measurement-induced logical gate using non-Gaussian resources to generate Schr"odinger cat states, providing an alternative to hybrid circuits and analyzing the quantum statistics and fidelity of the output states.

Contribution

It introduces a new scheme for preparing Schr"odinger cat states via a logical gate with non-Gaussian resources, offering detailed analysis and interpretation of the quantum statistics involved.

Findings

Gate conditionally produces superpositions of input states

High fidelity between output and ideal cat states achieved

Quantum statistics characterized by Wigner function analysis

Abstract

A measurement-induced continuous-variable logical gate is able to prepare Schr\"odinger 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 Schr\"odinger 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.