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

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).