Analog of the Clauser-Horne-Shimony-Holt inequality for steering

TL;DR

This paper derives a necessary and sufficient inequality for EPR-steering analogous to the CHSH Bell inequality, enabling the identification of steering in a specific quantum measurement scenario and analyzing experimental data.

Contribution

It introduces a new steering inequality that parallels the CHSH inequality, tailored for a scenario with specified measurements at Bob's site.

Findings

The inequality is strictly weaker than CHSH, as expected.

It can determine EPR-steering in experimental setups.

Applied to a recent experiment, it confirmed the presence of steering.

Abstract

The Clauser-Horne-Shimony-Holt (CHSH) inequality (and its permutations), are necessary and sufficient criteria for Bell nonlocality in the simplest Bell-nonlocality scenario: 2 parties, 2 measurements per party and 2 outcomes per measurement. Here we derive an inequality for EPR-steering that is an analogue of the CHSH, in that it is necessary and sufficient in this same scenario. However, since in the case of steering the device at Bob's site must be specified (as opposed to the Bell case in which it is a black box), the scenario we consider is that where Alice performs two (black-box) dichotomic measurements, and Bob performs two mutually unbiased qubit measurements. We show that this inequality is strictly weaker than the CHSH, as expected, and use it to decide whether a recent experiment [Phys. Rev. Lett. 110, 130401 (2013).] involving a single-photon split between two parties has demonstrated EPR-steering.