Local measurements on composite quantum systems can lead to correlations that cannot be explained by any means known to classical physics. This phenomenon, known as non-locality, not only shows that quantum and classical worlds dramatically depart one from another at the micro scale, but more importantly, serves as a powerful resource for interesting applications. In fact, non-locality lies at the heart of device-independent quantum information processing, a new paradigm for information processing aiming at designing protocols which do not rely on any assumptions on the devices used. Detection of non-locality and its characterization in composite quantum systems is one of the key problems in quantum information theory and central to the possibility of its full exploitation as a resource. In particular, the studies of non-locality in multipartite quantum systems are much less advanced than in the bipartite ones. An additional, though equally important, motivation to study multipartite systems is the recent progress in experimental realization of various many-body quantum states creating a platform for experimental implementation of theoretical predictions.
The overall aim of this project was therefore to significantly improve our understanding of the phenomenon of non-locality in multipartite quantum systems. The project was structured around three sub-projects, each defining more concrete objectives.
First, we aimed at understanding the relation between non-locality and entanglement—another key notion in quantum information—in the multipartite scenario. The second aim was to design methods of detection of non-locality in the multipartite scenario with the aid of quantities that are within reach of current experimental technology, and also to explore the phenomenon of non-locality in many-body interacting quantum systems. Finally, we aimed at addressing a more fundamental problem, that is, to propose information-theoretic principles allowing to single out the set of quantum correlations from the nonsignaling ones.
As for the first aim, we have provided a general construction of multipartite quantum states that are genuinely entangled but not genuinely non-local, thus showing that the inequivalence between entanglement and non-locality is a more generic feature of multipartite quantum systems than we thought. As for the second aim, we have introduced a general toolbox for studying non-locality in one-dimensional many-body interacting quantum systems with the aid of few-body correlations; within this approach the energy of a quantum many-body system can tell us whether it is non-local. We have also shown how the number of particles sharing genuine non-locality in a multipartite system can be certified from only two-body correlations. Finally, we have constructed a general class of Bell inequalities, involving an arbitrary number of measurements and outcomes, which are maximally violated by the maximally entangled states and provided numerical evidence that these inequalities can be used for self-testing.
