Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

TL;DR

This paper explores entropic steering criteria based on generalized entropic uncertainty relations, extending their application to Tsallis and Rényi entropies for bipartite and tripartite quantum systems, including GHZ and W states.

Contribution

It extends entropic steering criteria to Tsallis and Rényi entropies, providing new tools for detecting steerability in complex quantum systems.

Findings

Successfully applied criteria to GHZ and W states

Extended previous methods to new entropy types

Demonstrated effectiveness in bipartite and tripartite systems

Abstract

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.