# Negativity of quasiprobability distributions as a measure of nonclassicality

## TL;DR

This paper introduces a hierarchy of nonclassicality measures based on the negativity of s-parametrized quasiprobability distributions, providing an operational resource theory and a computable quantifier for nearly all nonclassical states.

## Contribution

It defines a continuous hierarchy of nonclassicality measures from quasiprobability negativity, establishing an operational resource theory and introducing a practical, computable quantifier.

## Key findings

- Negativity of quasiprobability distributions forms a hierarchy of nonclassicality measures.
- The negativity of the P-function has an operational interpretation as robustness.
- The proposed quantifier can identify nonclassicality in nearly all states.

## Abstract

We demonstrate that the negative volume of any $s$-paramatrized quasiprobability, including the Glauber-Sudashan $P$-function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures therefore belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan $P$-function in particular can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.