Directly estimating non-classicality

TL;DR

This paper introduces a practical method for directly measuring non-classicality in quantum states, requiring fewer measurements than full tomography, and demonstrates its effectiveness through optical experiments.

Contribution

It presents a novel approach to certify non-classicality using minimal measurements and provides a full certification framework based on Bochner's theorem and semi-definite programming.

Findings

Successful experimental demonstration with optical Fock states

Effective certification of non-classicality with limited measurements

Potential application in opto-mechanics for mechanical quantum states

Abstract

We establish a method of directly measuring and estimating non-classicality - operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows to certify non-classicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the non-classicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such features in mechanical degrees of freedom in opto-mechanics. The proof of the result is based on Bochner's theorem characterizing classical and quantum characteristic functions and on semi-definite programming. In this joint theoretical-experimental work we present data from experimental optical Fock state preparation, demonstrating the functioning of the approach.