Deriving Einstein-Podolsky-Rosen steering inequalities from the few-body Abner Shimony inequalities

TL;DR

This paper systematically derives EPR steering inequalities from Abner Shimony inequalities, demonstrating that EPR steering is a form of quantum nonlocality weaker than Bell-nonlocality, with specific bounds analyzed.

Contribution

It introduces a systematic method to derive EPR steering inequalities from AS inequalities and analyzes their bounds, clarifying the hierarchy of quantum nonlocality.

Findings

EPR steering inequalities have LHS bounds less than LHV bounds.

EPR steering is confirmed as weaker than Bell-nonlocality.

Derived inequalities provide new tools for quantum nonlocality tests.

Abstract

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell-nonlocality.