Nonlinear squeezing of superpositions of quadrature eigenstates

TL;DR

This paper introduces nonlinear squeezing operators for superpositions of quadrature eigenstates, providing a new way to detect non-Gaussianity and assess state approximations, with implications for quantum state fidelity and breeding protocols.

Contribution

It presents a novel family of operators exploiting symmetry in SQE states, linking nonlinear squeezing to non-Gaussianity and fidelity, and constructs optimal Fock space approximations.

Findings

Nonlinear squeezing serves as a witness of non-Gaussianity.

The measure correlates with quantum state fidelity.

Optimal approximations of SQE states are constructed in truncated Fock spaces.

Abstract

We introduce a family of operators exploiting the symmetry of superpositions of quadrature eigenstates (SQE) and demonstrate how the associated nonlinear squeezing, quantified by the expectation value of such operators, serves both as a witness of non-Gaussianity and as an indicator of the quality of SQE approximations. To establish the usefulness of this measure, we connect it to quantum state fidelity and evaluate its implications in breeding protocols. Finally, we construct optimal approximations of SQE states in truncated Fock spaces.