Black-box quantum information under spacetime symmetries

Quantum theory has not only revolutionized our understanding of physics, but it has also led to a multitude of technological applications in information theory. For example, quantum physics admits unconditionally secure cryptography or the generation of provably random numbers. In black box quantum information theory, this approach is taken one step further: security of cryptography or randomness can be guaranteed even if the devices involved in the protocol are untrusted (device-independence), or even if the validity of quantum theory itself is not taken for granted. In this setting, security follows solely from the observed statistics of the devices (seen as black boxes) and from simple physical principles, without any further assumptions. Previous research has focused on black boxes with abstract inputs and outputs, like abstract bits (zeros and ones) as commonly used in information theory. But in many actual experiments, the inputs and outputs are not abstract, but concrete spatiotemporal quantities like the spatial direction of a magnetic field, the duration of a pulse, or the angle of a polarizer. The goal of this project is to theoretically analyze the foundations and applications of such spatiotemporal black boxes. On the one hand, we hope that this analysis will give us fundamental insights into the relation between quantum theory, space and time: how do the statistical predictions of quantum theory fit into space and time? For example, do spatiotemporal symmetries constrain the probabilities of detector clicks, or the correlations between distant events, even without assuming the validity of quantum theory? What can we conclude with certainty if we build an experiment, set up temporal pulses or spatial fields, and then measure a certain statistics? Can we construct fundamentally new tests of quantum theory in this setting? On the other hand, we will explore how these insights can be put to use in quantum information theory, in particular in the context of semi-device-independent protocols. The security of such protocols is often based on abstract assumptions about the involved quantum systems, such as upper bounds on the information content of the transmitted systems. One goal of this research is to replace such abstract assumptions by more concrete, physically better motivated suppositions, in particular assumptions about the interplay of the systems with space and time. Furthermore, we hope to obtain new methods to detect the presence of so-called Bell nonlocality in realistic quantum systems.