One-sided Device-independent Self-testing of any Pure Two-qubit Entangled State

TL;DR

This paper introduces a method for self-testing any pure two-qubit entangled state in a one-sided device-independent manner using steering inequalities and correlation functions, advancing quantum certification techniques.

Contribution

It presents a novel approach combining steering inequalities and correlation measures to self-test all pure two-qubit entangled states in a 1-sided device-independent setting.

Findings

Maximal violation of fine-grained steering inequality certifies all pure two-qubit entangled states.

Violation of CHSH steering inequality aids in self-testing pure entangled states.

Correlation functions like mutual predictability are effective in state certification.

Abstract

We consider the problem of $1$-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the $2-2-2$ steering scenario (involving $2$ parties, $2$ measurement settings per party, $2$ outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of analogous CHSH inequality of steering or nonvanishing value of a quantity constructed using a correlation function called mutual predictability together with the maximal violation of fine-grained steering inequality can be used to self-test any pure entangled two-qubit state in a $1$-sided device-independent way.