Clauser-Horne Bell test with imperfect random inputs

TL;DR

This paper analyzes the randomness loophole in the Clauser-Horne Bell test, providing bounds on local hidden variable models with imperfect inputs, and offers insights applicable to various practical scenarios in quantum information experiments.

Contribution

It introduces a method to bound Bell values with partially random inputs in the Clauser-Horne test, addressing the randomness loophole in practical quantum experiments.

Findings

Explicit bounds on Bell values with imperfect randomness

Input randomness requirements quantified for practical scenarios

Analysis technique applicable to other Bell inequalities

Abstract

Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental test for the physics laws of nature, and on the other hand, it can be also applied in varieties of device independent tasks such as quantum key distribution and random number generation. In practice, loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions. In this work, we focus on the randomness (freewill) loophole and investigate the randomness requirement in a well-known Bell test, the Clauser-Horne test, under various conditions. With partially random inputs, we explicitly bound the Bell value for all local hidden variable models by optimizing the classical strategy. Our result thus puts input randomness requirement on the Clauser-Horne test under varieties of practical scenarios. The employed analysis technique can be generalized to other Bell's inequalities.