Robust one-sided self-testing of two-qubit states via quantum steering

TL;DR

This paper develops robust methods for verifying two-qubit entangled states using steering inequalities, improving noise tolerance and efficiency in one-sided device-independent quantum network verification.

Contribution

It introduces new steering inequalities with three measurement settings and provides analytical and numerical robustness bounds for self-testing two-qubit states.

Findings

Three-setting steering inequalities outperform two-setting ones in robustness.

Optimal local extraction maps achieve theoretical robustness bounds.

The protocols are sample-efficient for practical one-sided device-independent verification.

Abstract

Entangled two-qubit states are the core building blocks for constructing quantum communication networks. Their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. In this work we study the self-testing of two-qubit entangled states via steering inequalities, with robustness analysis against noise. More precisely, steering inequalities are constructed from the tilted Clauser-Horne-Shimony-Holt inequality and its general form, to verify the general two-qubit entangled states. The study provides a good robustness bound, using both local extraction map and numerical semidefinite-programming methods. In particular, optimal local extraction maps are constructed in the analytical method, which yields the theoretical optimal robustness bound. To further improve the robustness of one-sided self-testing, we propose a family of three measurement settings steering inequalities. The result shows that three-setting steering inequality demonstrates an advantage over two-setting steering inequality on robust self-testing with noise. Moreover, to construct a practical verification protocol, we clarify the sample efficiency of our protocols in the one-sided device-independent scenario.