Device independent state estimation based on Bell's inequalities

TL;DR

This paper presents a method to evaluate the quality and entanglement of an unknown quantum source solely based on the violation of Bell's inequalities, without needing to know the system's details.

Contribution

It introduces new fidelity measures and bounds for assessing quantum sources based on Bell inequality violations in a device-independent manner.

Findings

Derived bounds for fidelity measures based on Bell violation

Established a lower bound on entanglement from Bell violation

Provided a framework for device-independent source assessment

Abstract

The only information available about an alleged source of entangled quantum states is the amount $S$ by which the Clauser-Horne-Shimony-Holt (CHSH) inequality is violated: nothing is known about the nature of the system or the measurements that are performed. We discuss how the quality of the source can be assessed in this black-box scenario, as compared to an ideal source that would produce maximally entangled states (more precisely, any state for which $S=2\sqrt{2}$). To this end, we introduce several inequivalent notions of fidelity, each one related to the use one can make of the source after having assessed it; and we derive quantitative bounds for each of them in terms of the violation $S$. We also derive a lower bound on the entanglement of the source as a function of $S$ only.