Bell inequality violation in the presence of vacancies and incomplete measurements

TL;DR

This paper demonstrates that Bell inequality violations can be verified even with incomplete measurements affected by vacancies and detection inefficiencies, by optimizing measurement settings and accounting for errors.

Contribution

It introduces a method to verify Bell inequality violations under non-ideal, incomplete measurement conditions with high vacancy rates.

Findings

Bell inequality violation can be verified despite high vacancy rates.

The method is robust against imperfect state knowledge.

It tolerates moderate errors in state determination.

Abstract

The characterization of a quantum system can be complicated by non-ideal measurement processes. In many systems, the underlying physical measurement is only sensitive to a single fixed state, complementary outcomes are inferred by non-detection leaving them vulnerable to out-of-Hilbert space errors such as particle loss. It is still possible to directly verify the violation of a Bell inequality, hence witness entanglement of a bipartite state, in the presence of large vacancy rates using such an incomplete measurement by optimizing the measurement settings. The scheme is robust against imperfect a priori state knowledge and also moderate amounts of error in state determination.