Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information

TL;DR

This paper explores how improved entropic uncertainty relations, which incorporate state information, can lead to tighter and more effective EPR-steering inequalities, enhancing the ability to witness quantum steering.

Contribution

It derives correct EPR-steering inequalities from improved uncertainty relations that explicitly depend on the quantum state, and introduces a new symmetric EPR-steering inequality.

Findings

Improved uncertainty relations lead to tighter EPR-steering inequalities.

State-dependent bounds can be used to enhance steering detection.

A new symmetric EPR-steering inequality is developed.

Abstract

We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how the intrinsic uncertainty in a mixed quantum state is used to improve existing uncertainty relations and how this information affects one's ability to witness EPR-steering. As an example, we consider the recent improvement (using a quantum memory) to the entropic uncertainty relation between pairs of discrete observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of the tighter bound in the steering inequality leads to contradictions, due in part to the fact that the improved bound depends explicitly on the state being measured. By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one can use the information about the quantum state to improve our ability to witness EPR-steering, and develop a new symmetric EPR-steering inequality as a result.