Role of maximally entangled states in the context of linear steering inequalities

TL;DR

This paper establishes the conditions under which linear steering inequalities are violated in bipartite qubit systems and demonstrates that maximally entangled states produce the largest quantum violations for these inequalities.

Contribution

It provides necessary and sufficient conditions for violation of 2-settings linear steering inequalities and shows maximally entangled states yield the maximum violations for given observables.

Findings

Maximally entangled states produce the largest violations.

Necessary and sufficient conditions for inequality violation.

Maximal violations occur for maximally entangled states.

Abstract

Linear steering inequalities are useful to check whether a bipartite state is steerable when both the parties are allowed to perform $n$ dichotomic measurements on their parts. In the present study we propose the necessary and sufficient condition under which $2$-settings linear steering inequality will be violated for any given set of spin-$\frac{1}{2}$ observables at trusted and untrusted parties' sides. The important result revealed by the present paper is that maximally entangled two-qubit states give the largest quantum violations of $2$-settings as well as $3$-settings linear steering inequalities attainable for any given set of spin-$\frac{1}{2}$ observables at trusted and untrusted parties' sides (if any violation exists for that given set of spin-$\frac{1}{2}$ observables).