Randomness Requirement on CHSH Bell Test in the Multiple Run Scenario

TL;DR

This paper investigates the amount of randomness needed in CHSH Bell tests across multiple runs, emphasizing the importance of ruling out correlations to ensure reliable results in quantum nonlocality experiments.

Contribution

It provides a detailed analysis of the randomness requirements in CHSH Bell tests under different assumptions, highlighting the significance of eliminating correlations between runs.

Findings

Correlations between multiple runs affect test reliability

Ruling out inter-run correlations is crucial for valid Bell test results

Quantifies the randomness needed for different testing scenarios

Abstract

The Clauser-Horne-Shimony-Holt inequality test is widely used as a mean of invalidating the local deterministic theories and a tool of device independent quantum cryptographic tasks. There exists a randomness (freewill) loophole in the test, which is widely believed impossible to be closed perfectly. That is, certain random inputs are required for the test. Following a randomness quantification method used in literature, we investigate the randomness required in the test under various assumptions. By comparing the results, one can conclude that the key to make the test result reliable is to rule out correlations between multiple runs.