title: Unbounded Violation of Quantum Steering Inequalities.
abstract: We construct steering inequalities that exhibit unbounded violation. The concept was to exploit the relationship between steering violation and the uncertainty relation. To this end, we apply mutually unbiased bases and anticommuting observables, known to exhibit 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 anticommuting observables we are able to obtain a dichotomic steering inequality with unbounded violation. Thus far, there is no analogous result for Bell inequalities. Interestingly, both the dichotomic inequality and one of our inequalities cannot be directly obtained from existing uncertainty relations, which strongly suggest the existence of an unknown kind of uncertainty relation.
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.
authors.forename: M
authors.initials: M
authors.lastname: Marciniak
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: A
authors.initials: A
authors.lastname: Rutkowski
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|School of Mathematics and Statistics, Wuhan University, Wuhan, China.
authors.forename: Z
authors.initials: Z
authors.lastname: Yin
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: M
authors.initials: M
authors.lastname: Horodecki
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
authors.forename: R
authors.initials: R
authors.lastname: Horodecki