Optimal measurement bases for Bell-tests based on the CH-inequality

TL;DR

This paper investigates optimal measurement bases for Bell tests based on the CH-inequality, aiming to improve the trade-off between detection efficiency and violation strength using generalized Hardy bases.

Contribution

It introduces a generalization of Hardy measurement bases to optimize Bell tests with partially entangled states, enhancing detection efficiency and violation trade-offs.

Findings

Identifies measurement bases that optimize CH-inequality violation and detection efficiency.

Shows that generalized Hardy bases improve Bell test performance with partially entangled states.

Provides a framework for future Bell tests with entangled qubits.

Abstract

The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold detection efficiency, and the measurement settings adopted in the test. It is well known that the threshold efficiencies decrease when one considers partially entangled states and that the use of these states, unfortunately, generates a reduction in the CH violation. Nevertheless, these quantities are both dependent on the measurement settings considered, and in this paper we show that there are measurement bases which allow for an optimal situation in this trade-off relation. These bases are given as a generalization of the Hardy measurement bases, and they will be relevant for future Bell tests relying on pairs of entangled qubits.