Unbounded Violation of Quantum Steering Inequalities

M. Marciniak, A. Rutkowski, Z. Yin, M. Horodecki, and R. Horodecki
Phys. Rev. Lett. 115, 170401 – Published 20 October 2015
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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.

  • Received 24 May 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.170401

© 2015 American Physical Society

Authors & Affiliations

M. Marciniak1, A. Rutkowski1,2,*, Z. Yin3,1, M. Horodecki1,2, and R. Horodecki1,2

  • 1Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
  • 2National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland
  • 3School of Mathematics and Statistics, Wuhan University, Wuhan, China

  • *Corresponding author. fizar@ug.edu.pl

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Issue

Vol. 115, Iss. 17 — 23 October 2015

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