Bell's Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality

TL;DR

This paper demonstrates that Bell's nonlocality can be detected through the violation of steering inequalities, offering a new approach that may simplify Bell tests and avoid loopholes.

Contribution

It introduces a novel method to identify Bell nonlocal states using steering inequalities, expanding the tools for studying quantum nonlocality.

Findings

Bell nonlocal states can be constructed from steerable states.

Steering inequality violation can detect Bell's nonlocality.

A nine-setting steering inequality enhances detection efficiency.

Abstract

Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell's nonlocality. Among which, Bell's nonlocality is the strongest type. Bell's nonlocality for quantum states is usually detected by violation of some Bell's inequalities, such as Clause-Horne-Shimony-Holt inequality for two qubits. Steering is a manifestation of nonlocality intermediate between entanglement and Bell's nonlocality. This peculiar feature has led to a curious quantum phenomenon, the one-way Einstein-Podolsky-Rosen steering. The one-way steering was an important open question presented in 2007, and positively answered in 2014 by Bowles \emph{et al.}, who presented a simple class of one-way steerable states in a two-qubit system with at least thirteen projective measurements. The inspiring result for the first time theoretically confirms quantum nonlocality can be fundamentally asymmetric. Here, we propose another curious quantum phenomenon: Bell nonlocal states can be constructed from some steerable states. This novel finding not only offers a distinctive way to study Bell's nonlocality without Bell's inequality but with steering inequality, but also may avoid locality loophole in Bell's tests and make Bell's nonlocality easier for demonstration. Furthermore, a nine-setting steering inequality has also been presented for developing more efficient one-way steering and detecting some Bell nonlocal states.