The Schr & ouml;dinger-Newton (SN) model is a semi-classical theory in which, inaddition to mutual attraction, massive quantum particles interact with theirown gravitational fields. While there are many studies on the phenomenologyof single particles, correlation dynamics in multipartite systems is largely unexplored. Here, we show that the SN interactions preserve the product form of the initial state of a many-body system, yet on average agreeing with classicalmechanics of continuous mass distributions. This leads to a simple test of themodel, based on verifying bipartite gravitational evolution towards non-productstates. We show using standard quantum mechanics that, with currently access-ible single-particle parameters, two masses released from harmonic traps getcorrelated well before any observable entanglement is accumulated. Therefore,the SN model can be tested with setups aimed at observation of gravitationalentanglement with significantly relaxed requirements on coherence time. Wealso present a mixed-state extension of the model that avoids superluminal signaling

While a wide variety of astrophysical and cosmological phenomena suggest the presence of Dark Matter, all evidence remains via its gravitational effect on the known matter. As such, it is conceivable that this evidence could be explained by a modification to gravitation and/or concepts of inertia. Various formulations of modified gravity exist, each giving rise to several non-canonical outcomes. This motivates us to propose an experiment searching for departures from (quantum) Newtonian predictions in a bipartite setting with gravitational accelerations $\lesssim 10^{-10}$ m/s$^2$, i.e., where the effective force needs to be stronger than Newtonian to account for the Dark Matter effects. Since quantum particles naturally source weak gravitation, their non-relativistic dynamics offers opportunities to test this small acceleration regime. We show that two nearby mesoscopic quantum masses accumulate significantly larger entanglement in modified gravity models, such as the Modified Newtonian Dynamics. Our calculations include Casimir-Polder forces as well as tidal effects next to the surface of the earth, and confirm that entanglement is observable within the limits imposed by environmental decoherence. We demonstrate how the temperature can be fine-tuned such that modified gravity is certified simply by witnessing the entanglement generated from uncorrelated thermal states, eliminating the need for precise noise characterization. Overall, the required parameters could be realized in a tabletop experiment.

Due to the weakness of gravitational coupling, all quantum experiments up to date in which gravity plays a role utilized the field of the Earth. Since this field undergoes practically undetectable back-action from quantum particles, it effectively admits a classical description as a fixed background Newtonian field or spacetime. This argument strongly motivates theoretical and experimental research towards a demonstration of gravitation between two quantum masses, as this is one of the most straightforward scenarios where quantum features of gravity could be observed. Several proposals studied the possibility of generating entanglement between two massive objects. Along the same lines, with a particular focus on gravity, this thesis introduces general tools to tackle interaction-mediated entanglement and applies them to two particles prepared in continuous-variable states.

We describe a complete method for a precise study of gravitational interaction between two nearby quantum masses. Since the displace-ments of these masses are much smaller than the initial separation between their centers, the displacement-to-separation ratio is a nat-ural parameter in which the gravitational po-tential can be expanded. We show that entan-glement in such experiments is sensitive to ini-tial relative momentum only when the system evolves into non-Gaussian states, i.e., when the potential is expanded at least up to the cubic term. A pivotal role of force gradient as the dominant contributor to position-momentum correlations is demonstrated. We establish a closed-form expression for the entanglement gain, which shows that the contribution from the cubic term is proportional to momentum and from the quartic term is proportional to momentum squared. From a quantum infor-mation perspective, the results find applica-tions as a momentum witness of non-Gaussian entanglement. Our methods are versatile and apply to any number of central interactions ex-panded to any order.