Increasing the statistical significance of entanglement detection in experiments

TL;DR

This paper shows that optimizing entanglement inequalities for higher violation does not always improve detection significance when considering statistical errors, and proposes methods to enhance entanglement test significance.

Contribution

It reveals that reducing inequality violation can increase statistical significance and offers a new approach to develop entanglement tests with higher significance.

Findings

Reducing violation can improve statistical significance.

Experimental validation with four-photon tests.

Proposed method for high-significance entanglement detection.

Abstract

Entanglement is often verified by a violation of an inequality like a Bell inequality or an entanglement witness. Considerable effort has been devoted to the optimization of such inequalities in order to obtain a high violation. We demonstrate theoretically and experimentally that such an optimization does not necessarily lead to a better entanglement test, if the statistical error is taken into account. Theoretically, we show for different error models that reducing the violation of an inequality can improve the significance. Experimentally, we observe this phenomenon in a four-photon experiment, testing the Mermin and Ardehali inequality for different levels of noise. Furthermore, we provide a way to develop entanglement tests with high statistical significance.