# Characterization of the quantumness of unsteerable tripartite correlations

## TL;DR

This paper introduces the concept of super-bi-unsteerability to characterize the genuine quantumness of tripartite correlations unsteerable across all bipartite cuts, extending the idea of super-unsteerability.

## Contribution

It generalizes super-unsteerability to tripartite systems, defining and exemplifying genuine super-bi-unsteerability as a new tool for quantumness characterization.

## Key findings

- Defined super-bi-unsteerability for tripartite correlations.
- Presented examples of genuine super-bi-unsteerability.
- Provided a new method to quantify tripartite quantum correlations.

## Abstract

Quantumness for a bipartite unsteerable quantum correlation is operationally characterized by the notion of super-unsteerability. Super-unsteerability refers to the requirement of a larger dimension of the random variable that the steering party has to preshare with the party to be steered in the classical simulation protocol to generate an unsteerable correlation than the local Hilbert space dimension of the quantum states (reproducing the given unsteerable correlation) at the steering party's side. In the present study, this concept of super-unsteerability is generalized by defining the notion of super-bi-unsteerability for tripartite correlations, which is unsteerable across a bipartite cut. Genuine super-bi-unsteerability is defined as the occurrence of super-bi-unsteerability across all possible bipartite cuts. Specific example of genuine super-bi-unsteerability for tripartite correlations has been presented. This study provides a tool to characterize the genuine quantumness of tripartite quantum correlations which are unsteerable across every bipartite cut.