Challenging preconceptions about Bell tests with photon pairs

Understand

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.