# Diagnosing steerability of a bipartite state with the nonsteering threshold

## TL;DR

This paper introduces a new method using averaged fidelity and nonsteering thresholds to diagnose steerability in bipartite quantum states, providing a general scheme for designing linear steering criteria and optimal measurements.

## Contribution

It develops a comprehensive scheme to determine steerability using averaged fidelity and nonsteering thresholds, including strategies for optimal measurement design.

## Key findings

- Defined nonsteering threshold to quantify steerability
- Established criteria for steerability based on averaged fidelity
- Provided methods for optimal measurement design in different scenarios

## Abstract

In the present work, a traditional quantity, the averaged fidelity, is introduced as the steering parameter. From the definitions of steering from Alice to Bob and the joint measurability, a general scheme is developed to design linear steering criteria. For a given set of measurements on Bob's side, the so-called nonsteering threshold is defined to quantify the ability to detect steering. If the measured averaged fidelity exceeds this threshold, it is shown that the state shared by Alice and Bob is steerable from Alice to Bob, and the measurements performed by Alice are also verified to be incompatible. Within the general scheme, a discussion about how to design optimal criteria is provided for two different scenarios: (a) to find the optimal measurements on Bob's side when the state is unknown and (b) to find the optimal measurements for Alice when the state and the measurements on Bob's side are given.