Negativity and steering: a stronger Peres conjecture

TL;DR

This paper demonstrates that all studied EPR-steering inequalities require negativity for violation, supporting a strengthened version of Peres' conjecture linking negativity to Bell inequality violations.

Contribution

The paper adapts semidefinite programming techniques to EPR-steering, showing negativity is necessary for violating steering inequalities, thus strengthening Peres' conjecture.

Findings

All studied steering inequalities require negativity for violation.

Supports a stronger form of Peres' conjecture.

Adapts quantitative entanglement certification methods to steering.

Abstract

The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et. al. showed how to make this statement quantitative, using semidefinite programming to calculate how much entanglement is certified by a given violation. Here I adapt their techniques to the case where Bob's measurement devices are in fact trusted, the setting for "EPR-steering" inequalities. Interestingly, all of the steering inequalities studied turn out to require negativity for their violation. This supports a significant strengthening of Peres' conjecture that negativity is required to violate a bipartite Bell inequality.