Bell inequalities violated using detectors of low efficiency

TL;DR

This paper introduces a family of Bell inequalities that require the lowest detection efficiency for violation, providing upper bounds on the critical efficiency needed for observing quantum nonlocality with low-efficiency detectors.

Contribution

It defines a new family of Bell inequalities with minimal detection efficiency requirements, extending previous work and establishing bounds for quantum violations with low-efficiency detectors.

Findings

Provides upper bounds for critical detection efficiency for Bell inequality violations.

Shows that near the threshold efficiency, the violating state approaches a product state of qubits.

Extends known inequalities for the case m>2, highlighting gaps between bounds.

Abstract

We define a family of binary outcome $n$-party $m\leq n$ settings per party Bell inequalities whose members require the least detection efficiency for their violation among all known inequalities of the same type. This gives upper bounds for the minimum value of the critical efficiency --- below which no violation is possible --- achievable for such inequalities. For $m=2$, our family reduces to the one given by Larsson and Semitecolos in 2001. For $m>2$, a gap remains between these bounds and the best lower bounds. The violating state near the threshold efficiency always approaches a product state of $n$ qubits.