Challenging preconceptions about Bell tests with photon pairs

TL;DR

This paper challenges common assumptions in Bell tests with photon pairs, showing that maximal violation does not require perfect detectors or maximally entangled states, and provides optimal parameters to close loopholes.

Contribution

It demonstrates that traditional beliefs about conditions for maximal Bell violation are incorrect and offers a comprehensive method to optimize Bell tests with photon pairs under realistic conditions.

Findings

Maximal CHSH violation does not require perfect detectors.

Optimal parameters can close loopholes in photon-based Bell tests.

Non-maximally entangled states can achieve maximal violation under certain conditions.

Abstract

Motivated by very recent experiments, we consider a scenario "\`a la Bell" in which two protagonists test the Clauser-Horne-Shimony-Holt (CHSH) inequality using a photon-pair source based on spontaneous parametric down conversion and imperfect photon detectors. The conventional wisdom says that (i) if the detectors have unit efficiency, the CHSH violation can reach its maximum quantum value $2\sqrt{2}$. To obtain the maximal possible violation, it suffices that the source emits (ii) maximally entangled photon pairs (iii) in two well defined single modes. Through a non-perturabive calculation of non-local correlations, we show that none of these statements are true. By providing the optimal pump parameters, measurement settings and state structure for any detection efficiency and dark count probability, our results give the recipe to close all the loopholes in a Bell test using photon pairs.