# Quantum steering with positive operator valued measures

## TL;DR

This paper investigates quantum steering with POVMs, formulating steerability as a convex nesting problem, and provides numerical evidence that two-qubit Werner states are unsteerable with POVMs up to a certain mixing probability.

## Contribution

It introduces a convex nesting framework for assessing steerability with POVMs and applies it to Werner states, strengthening theoretical understanding and providing numerical evidence.

## Key findings

- Steerability with POVMs can be formulated as a convex nesting problem.
- Werner states are unsteerable with POVMs up to a mixing probability of 1/2.
- Numerical methods confirm unsteerability within a small error margin.

## Abstract

We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of determining the steerability of a bipartite quantum state of finite dimension with POVMs can be formulated as a nesting problem of two convex objects. One consequence of this is the strengthening of the theorem that justifies choosing the LHS ensemble based on symmetry of the bipartite state. As a more practical application, we study the classic problem of the steerability of two-qubit Werner states with POVMs. We show strong numerical evidence that these states are unsteerable with POVMs up to a mixing probability of $\frac{1}{2}$ within an accuracy of $10^{-3}$.