Quantum information theory has several puzzling properties.  In particular, it predicts that information carried by quantum objects is incompatible with the use of the logical ‘or’. While in our intuition of the world, a cat hidden in a box can be dead or alive, according to quantum mechanics this assertion is not valid anymore.  Hence, we need a new concept: we say that a quantum cat can be dead ‘and’ alive. This new concept is however hard to accept: couldn’t we imagine a new theory replacing quantum information theory and compatible again with our stadard logical ‘or’?  In 1964, Bell proved that, in some sense, this puzzling feature of quantum theory is a necessity : there does not exist any ‘reasonable’ theory of information (which would replace quantum information theory) compatible with this logical ‘or’.
Bell’s seminal proof is based on quantum correlations, which are obtained when multiple parties perform independent measurements on a shared quantum state.
I’ll first review this Bell theorem, and discuss some of its main consequences for the foundations of physics and the more philosophical notion of determinism and randomness. Then, I will discuss recent generalization of this theorem which were obtained in the context of quantum networks, in which multiple parties perform independent measurements on several, independent quantum states.
In particular, I’ll show that Real Quantum Theory (the theory obtained replacing complex by real numbers in standard Quantum Information Theory) can be ruled out by a Bell-like experiment.

This talk is based on "La non-localité quantique à l’ère des réseaux, Marc-Olivier Renou, Nicolas Brunner et Nicolas Gisin, POUR LA SCIENCE N° 528 (20 septembre 2021)" and "Les nombres imaginaires sont indispensables à la théorie quantique pour décrire le monde, Marc-Olivier Renou, Antonio Acin et Miguel Navascués, POUR LA SCIENCE N° 551, 30 août 2023"