# Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes

## TL;DR

This paper introduces a new method to quantify Einstein-Podolsky-Rosen steering using extremal boxes, providing a convex measure called steering cost, applicable in scenarios with black-box and projective measurements.

## Contribution

It develops a novel approach to detect and quantify EPR steering via extremal boxes and introduces the steering cost as a convex monotone measure.

## Key findings

- The method effectively detects steerability in specific measurement scenarios.
- Steering cost is demonstrated as a convex steering monotone.
- Application to measurement correlations reveals their steerability levels.

## Abstract

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality which is weaker than Bell nonlocality, but stronger than entanglement. Here we present a method to check Einstein-Podolsky-Rosen steering in the scenario where the steering party performs two black-box measurements and the trusted party performs projective qubit measurements corresponding to two arbitrary mutually unbiased bases. This method is based on decomposing the measurement correlations in terms of extremal boxes of the steering scenario. In this context, we propose a measure of steerability called steering cost. We show that our steering cost is a convex steering monotone. We illustrate our method to check steerability with two families of measurement correlations and find out their steering cost.