Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios

TL;DR

This paper reviews how detection efficiency impacts the demonstration of non-classicality in various quantum scenarios, highlighting thresholds, challenges, and how different structures influence efficiency requirements.

Contribution

It provides a comprehensive analysis of detection efficiency bounds across multiple (semi-)device-independent quantum scenarios, including recent insights into efficiency relaxations.

Findings

Detection thresholds vary across scenarios, e.g., 2/3 for CHSH.

Multiple sources can relax efficiency requirements in bilocality.

Efficiency impacts security in quantum key distribution.

Abstract

This article provides a comprehensive review of the critical role of detection efficiency in demonstrating non-classicality across various device-independent and semi-device-independent scenarios. The central focus is the detection loophole, a challenge in which imperfect detectors can allow classical hidden variable models to mimic quantum correlations, thus masking genuine non-classicality. As a review, the article revisits the paradigmatic Bell scenario, detailing the efficiency requirements for the CHSH inequality, such as the 2/3 threshold for symmetric efficiencies, and traces the historical trajectory toward the first loophole-free tests. The analysis extends to other causal structures to explore how efficiency requirements are affected in different contexts. These include the instrumental scenario, which for binary variables has recently been shown to follow the same inefficiency bounds as the bipartite dichotomic Bell scenario; the prepare-and-measure scenario, where inefficiencies impact the certification of a quantum system's dimension and create security breaches in protocols such as Quantum Key Distribution (QKD); and the bilocality scenario, which exemplifies how employing multiple independent sources can significantly relax the required efficiencies to certify non-classical correlations.