Requirements for a loophole-free photonic Bell test using imperfect setting generators

TL;DR

This paper analyzes the requirements for conducting a loophole-free photonic Bell test, addressing multiple loopholes and the impact of imperfect random number generators on the test's validity.

Contribution

It provides a comprehensive analysis of closing all major loopholes in photonic Bell tests and adapts statistical methods for imperfect setting generators.

Findings

Identifies conditions to close all loopholes simultaneously.

Proposes modifications to Bell inequalities for imperfect randomness.

Provides statistical analysis framework for realistic experimental setups.

Abstract

Experimental violations of Bell inequalities are in general vulnerable to so-called "loopholes." In this work, we analyse the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e. detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to non-ideal random number generators. We discuss necessary adaptations of the CH/Eberhard inequality when using such imperfect devices and -- using Hoeffding's inequality and Doob's optional stopping theorem -- the statistical analysis in such Bell tests.