Detection loophole in quantum causality and its countermeasures

TL;DR

This paper investigates the detection efficiency needed to observe quantum causality violations, deriving new inequalities that lower the required detection thresholds compared to previous bounds, thus facilitating experimental tests.

Contribution

It introduces new classical and quantum causal inequalities with reduced detection efficiency requirements, advancing the feasibility of experimental quantum causality demonstrations.

Findings

Classical causal inequalities require over 95% detection efficiency for violation.

New inequalities reduce the detection efficiency requirement to around 92% for quantum correlations.

Quantum causal inequalities show lower detection thresholds than Bell inequalities, aiding experimental realization.

Abstract

Quantum causality violates classical intuitions of cause and effect and is a unique quantum feature different from other quantum phenomena such as entanglement and quantum nonlocality. In order to avoid the detection loophole in quantum causality, we initiate the study of the detection efficiency requirement for observing quantum causality. We first show that previous classical causal inequalities require detection efficiency at least 95.97% (89.44%) to show violation with quantum (nonsignaling) correlations. Next we derive a classical causal inequality I_{222} and show that it requires lower detection efficiency to be violated, 92.39% for quantum correlations and 81.65% for nonsignaling correlations, hence substantially reducing the requirement on detection. Then we extend this causal inequality to the case of multiple measurement settings and analyze the corresponding detection efficiency. After that, we show that previous quantum causal inequalities require detection efficiency at least 94.29% to violate with nonsignaling correlations. We subsequently derive a quantum causal bound J_{222} that has a lower detection efficiency requirement of 91.02% for violation with nonsignaling correlations. Our work paves the way towards an experimental demonstration of quantum causality and shows that causal inequalities significantly differ from Bell inequalities in terms of the detection efficiency requirement.