title: Increasing the statistical significance of entanglement detection in experiments.
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.
authors.affiliation: Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21A, A-6020 Innsbruck, Austria.
authors.forename: Bastian
authors.initials: B
authors.lastname: Jungnitsch
authors.forename: Sönke
authors.initials: S
authors.lastname: Niekamp
authors.forename: Matthias
authors.initials: M
authors.lastname: Kleinmann
authors.forename: Otfried
authors.initials: O
authors.lastname: Gühne
authors.forename: He
authors.initials: H
authors.lastname: Lu
authors.forename: Wei-Bo
authors.initials: WB
authors.lastname: Gao
authors.forename: Yu-Ao
authors.initials: YA
authors.lastname: Chen
authors.forename: Zeng-Bing
authors.initials: ZB
authors.lastname: Chen
authors.forename: Jian-Wei
authors.initials: JW
authors.lastname: Pan