# Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

## TL;DR

This paper proposes a method to quantify nonlinear squeezing in mechanical oscillators within quantum optomechanics, demonstrating that noise reduction below classical levels indicates nonclassical states suitable for quantum information processing.

## Contribution

It introduces a scheme to reconstruct nonlinear squeezing in linear quantum optomechanics and analyzes the impact of decoherence on this nonlinear quantum resource.

## Key findings

- Nonlinear squeezing can be reconstructed in standard optomechanical systems.
- Mechanical states with reduced nonlinear quadrature noise are nonclassical.
- Decoherence affects the ability to observe nonlinear squeezing.

## Abstract

Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian ancilla. A necessary condition for a nonlinear phase state to implement a nonlinear phase gate is that noise in a selected nonlinear quadrature should decrease below the level of classical states. A reduction of the variance in this nonlinear quadrature below the ground state of the ancilla, a type of nonlinear squeezing, is the resource embedded in these non-Gaussian states and a figure of merit for nonlinear quantum processes. Quantum optomechanics with levitating nanoparticles trapped in nonlinear optical potentials is a promising candidate to achieve such resources in a flexible way. We provide a scheme for reconstructing this figure of merit, which we call nonlinear squeezing, in standard linear quantum optomechanics, analysing the effects of mechanical decoherence processes on the reconstruction and show that all mechanical states which exhibit reduced noise in this nonlinear quadrature are nonclassical.