Detection-loophole-free nonlocality in the simplest scenario

TL;DR

This paper establishes minimal efficiency and complexity thresholds for loophole-free quantum nonlocality detection using two-qubit states, demonstrating that only one detector with moderate efficiency is needed, confirmed by a photonic experiment.

Contribution

It identifies fundamental thresholds for quantum steering with minimal detector requirements, simplifying loophole-free nonlocality tests compared to Bell tests.

Findings

Threshold efficiency for steering: > 1/X with X settings.

Loophole-free experiment achieved with 51.6% detector efficiency.

Applicable to all pure entangled states, unlike Bell tests.

Abstract

Loophole-free quantum nonlocality often demands experiments with high complexity (defined by all parties' settings and outcomes) and multiple efficient detectors. Here, we identify the fundamental efficiency and complexity thresholds for quantum steering using two-qubit entangled states. Remarkably, it requires only one photon detector on the untrusted side, with efficiency $\epsilon > 1/X$, where $X \geq 2$ is the number of settings on that side. This threshold applies to all pure entangled states, in contrast to analogous Bell-nonlocality tests, which require almost unentangled states to be loss-tolerant. We confirm these predictions in a minimal-complexity ($X = 2$ for the untrusted party and a single three-outcome measurement for the trusted party), detection-loophole-free photonic experiment with $\epsilon = (51.6 \pm 0.4)\% $.