Unbounded violation of quantum steering inequalities

TL;DR

This paper constructs quantum steering inequalities with unbounded violations using mutually unbiased bases and anti-commuting observables, revealing new insights into quantum uncertainty and steering phenomena.

Contribution

It introduces a constructive method to achieve unbounded violations of steering inequalities, including dichotomic cases, surpassing previous operator space theory approaches.

Findings

Unbounded violation of steering inequalities demonstrated.

Dichotomic steering inequality with unbounded violation obtained.

Results suggest existence of new, unknown uncertainty relations.

Abstract

We construct steering inequalities which exhibit unbounded violation. The concept was to exploit the relationship between steering violation and uncertainty relation. To this end we apply mutually unbiased bases and anti-commuting observables, known to exibit the strongest uncertainty. In both cases, we are able to procure unbounded violations. Our approach is much more constructive and transparent than the operator space theory approach employed to obtain large violation of Bell inequalities. Importantly, using anti-commuting observables we are able to obtain a {\it dichotomic} steering inequality with unbounded violation. So far there is no analogous result for Bell inequalities. Interestingly, both the dichotomic inequality and one of our inequalities can not be directly obtained from existing uncertainty relations, which strongly suggest the existence of an unknown kind of uncertainty relation.