Unquestionable Bell theorem for interwoven frustrated down conversion processes (2508.19207v1)

Abstract: In the Wang et al. paper "Violation of Bell inequality with unentangled photons'' [Science Advances, 1 Aug 2025 Vol 11, Issue 31], in which a brilliant experiment involving two interwoven frustrated down conversion processes is reported, Bell non-classicality of the observed interference processes is conjectured under some tacit additional assumptions. To clear any doubts about Bell non-classicality of the interference processes observed by Wang et al., we give an unconditional Bell-type proof that a modified version of the experiment indeed would reveal a violation of local realism. The data of the Wang et al. experiment show destructive interference which surpasses the required threshold for Bell non-classicality in the modified version, and thus effectively constitutes a positive experimental Bell non-classicality test employing our proposal. The essence of our method is to abandon the usual approach in which macroscopically controlled optical phases define the measurement settings in a Bell experiment. Instead, in our case, the local settings are determined by switching on or off the local pumping fields of the parametric down conversion crystals at the local measuring stations of "Alice and Bob''. We also show that in a standard framework of local hidden variable theories that do not require any additional assumptions, it is possible to construct a local realistic model which exactly reproduces the probabilities on which the conjecture by Wang et al. violation of local realism was based. Thus, we prove that the tacit additional assumptions in the Bell analysis of Wang et al. constrain the class of local realistic models refuted by the experiment. Also, we claim that the non-classical effects in the Wang et al. experiment cannot be ascribed to unentangled photons.