EPR Steering Inequalities from Entropic Uncertainty Relations

TL;DR

This paper develops new entropic uncertainty relation-based inequalities to detect and analyze EPR steering in quantum systems, including symmetric, one-way, and POVM-based scenarios, revealing nuanced correlation properties.

Contribution

It introduces novel entropic steering inequalities applicable to diverse quantum measurements and explores their implications for asymmetric and symmetric EPR steering.

Findings

Derived entropic inequalities for EPR steering detection

Extended inequalities to POVMs and hybrid degrees of freedom

Analyzed one-way and symmetric steering distinctions

Abstract

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.