# Operational characterization of quantumness of unsteerable bipartite states

## TL;DR

This paper introduces the concept of super-unsteerability to quantify the quantumness of unsteerable correlations, showing that some unsteerable states require higher-dimensional classical resources to simulate than their quantum origin.

## Contribution

It generalizes the notion of superlocality to unsteerable correlations, defining super-unsteerability as a new way to measure quantumness in these states.

## Key findings

- Certain unsteerable states exhibit super-unsteerability.
- Super-unsteerability indicates a higher classical dimension needed for simulation.
- Provides a framework for quantifying quantumness in convex operational theories.

## Abstract

Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A {\bf 95}, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as \textit{super-correlation}, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be super-correlated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of \textit{super-unsteerability}, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.