Operator space approach to steering inequality

TL;DR

This paper applies operator space theory to bipartite steering inequalities, demonstrating unbounded violations with explicit constructions, especially using non-maximally entangled states, highlighting a key difference from Bell inequalities.

Contribution

It introduces a novel operator space approach to steering inequalities, showing unbounded violations and explicit constructions, particularly in the bipartite dichotomic case.

Findings

Unbounded largest violation of steering inequality achieved

Explicit construction of steering functionals

Difference from Bell inequalities with bounded violations

Abstract

In \cite{JP2011,JPPVW2010} the operator space theory was applied to study bipartite Bell inequalities. The aim of the paper is to follow this line of research and use the operator space technique to analyze the steering scenario. We obtain a bipartite steering functional with unbounded largest violation of steering inequality, as well as we can construct all ingredients explicitly. It turns out that the unbounded largest violation is obtained by non maximally entangled state. Moreover, we focus on the bipartite dichotomic case where we construct a steering functional with unbounded largest violation of steering inequality. This phenomenon is different to the Bell scenario where only bounded largest violation can be obtained by any bipartite dichotomic Bell functional.