Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity

TL;DR

This paper proposes a new distance-based measure for quantifying nonclassicality in bosonic field states, based on operator ordering sensitivity, which better captures quantum features than previous measures.

Contribution

It introduces the operator ordering sensitivity as a novel metric for nonclassicality, providing a more accurate and geometric way to distinguish quantum states.

Findings

The new measure outperforms existing nonclassicality measures.

Operator ordering sensitivity captures oscillations in the Wigner function.

The measure is linked but distinct from quantum macroscopicity.

Abstract

We introduce a new distance-based measure for the nonclassicality of the states of a bosonic field, which outperforms the existing such measures in several ways. We define for that purpose the operator ordering sensitivity of the state which evaluates the sensitivity to operator ordering of the Renyi entropy of its quasi-probabilities and which measures the oscillations in its Wigner function. Through a sharp control on the operator ordering sensitivity of classical states we obtain a precise geometric image of their location in the density matrix space allowing us to introduce a distance-based measure of nonclassicality. We analyse the link between this nonclassicality measure and a recently introduced quantum macroscopicity measure, showing how the two notions are distinct.