Generalized contextuality in large quantum systems

Quantum theory promises technological applications that would be impossible within classical physics: faster computation, more accurate metrology, or the generation of provably secure random numbers. However, to make this work, we first need to test whether our devices are really quantum and work as desired a task called certification. This is not only relevant for technology, but also for fundamental physics: given some large physical system, such as a Bose-Einstein condensate, how can we prove that its properties cannot be explained by classical physics? In other words, how can we certify its nonclassicality? In this project, we will develop a new method to do so, both theoretically (via mathematical proofs and conceptual argumentation) and experimentally (with concrete data supplied by colleagues at ETH Zurich). Our approach is based on the phenomenon of contextuality: properties of quantum systems cannot be independent of the choice of implementation of the measurement procedures. In other words, if we ask Nature a question, then the answer must sometimes depend on the experimental context. Here, we develop methods that allow us to certify this phenomenon in physical systems even if they are very large and can only be probed in coarse and incomplete ways, and even if we know nothing about their composition, time evolution, or the physical theory that describes them. Our project will improve upon earlier work in several respects. Most earlier attempts to certify nonclassicality in large quantum systems have relied on the notion of Bell nonlocality: correlations between several particles cannot be explained by any local hidden- variable model. However, this has only been possible under strong additional assumptions, since it is impossible to measure all particles of a large quantum system individually. Moreover, both the experimental detection as well as the theoretical definition of contextuality (in the sense that is relevant for our project) has been restricted to situations in which the experimenter can measure all properties of the physical system completely and exhaustively (tomographic completeness). In our project, we will drop these assumptions and develop methods that are device- and theory-independent and that work with coarse and incomplete experimental data. Our projects spans quantum physics from its philosophical foundations up to its experimental implementation. Conceptually, we will shed light on the question of how coarse experimental data can render a microscopic theory implausible. Mathematically, we will develop methods that can certify this notion of contextuality with algorithms and inequalities. Finally, we will apply our results to concrete experimental data from nanomechanical oscillators and Bose-Einstein condensates.