Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

TL;DR

This paper establishes a fundamental link between EPR steering and Bell's nonlocality, proposing a new approach to test Bell's nonlocality via steering inequalities, potentially enabling loophole-free Bell tests.

Contribution

It introduces a theorem connecting EPR steerability of a mapped state to Bell nonlocality of the original state, offering a novel method to test Bell's nonlocality without CHSH inequality.

Findings

EPR steerability implies Bell nonlocality for two-qubit states.

A new approach to test Bell's nonlocality through steering inequalities.

Potential for loophole-free Bell-test experiments without CHSH inequality.

Abstract

Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $\tau$, if its mapped state $\rho$ is EPR steerable, then the state $\tau$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.