Approccio algebrico per verificare la non-classicality oltre la Teoria Quantistica

Recently, new witnesses of non-classicality that go beyond the usual quantum information schemes have been proposed by [58]. These witnesses are the essential theoretical underpinning of a brand-new experimental proposal to test quantum effects in gravity, such that it works that works under minimal assumptions about gravity itself. The key idea is that if gravity can entangle two masses, then itself must have non-classical features - specifically, it must have at least two incompatible variables. In this thesis a more general algebraic approach to the above-mentioned witnesses is provided by studying a group-theoretical formalism for quantum mechanics and extending its validity also to classical mechanics. The main objects of study will be hybrid quantum-classical systems and, in passing, erroneous claims that a quantum-classical hybrid can generate entanglement are refuted, thus vindicating the validity of the witnesses. This study opens new directions for the research of a consistent theory of the hybrid interaction by establishing the distinction between quantum and classical systems in their group- theoretical formulation.