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.

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. 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. In our project, we have theoretically analyzed the foundations and applications of such "spatiotemporal black boxes". We have gained exciting insights into the foundations of, in particular, those black boxes which can be rotated in space: in many cases, their statistical behavior can be determined directly from rotational symmetry and the result agrees with the quantum predictions without having used quantum theory in the calculation. This motivates the exciting conjecture that at least parts of quantum physics can be derived from properties of spacetime. On the other hand, we were able to show that for sufficiently complicated "metrological games" (in which a player must determine properties of a rotation angle by measurement), theories beyond quantum physics are conceivable that allow higher winning probabilities. Based on these fundamental insights, we were able to develop two methods for generating secure random numbers: a protocol that relies on spatial rotations and another one that relies on time evolution and uses quantum speed limits as a certification tool. The former protocol has the advantage that its security does not depend on the validity of quantum mechanics, and the latter that it is based on an arguably simpler and physically better motivated assumption (about the energy uncertainty of the system) than comparable previous works. We have also gained exciting insights into how local rotational symmetry (with global symmetry under permutations) can be used to characterize Bell nonlocality in many-body systems. Our approach has also led us to propose a novel test of quantum theory that decides directly from the statistics of measurement data whether a quantum explanation of the data is plausible or not. In addition to further insights into the connection between non-classicality and symmetry, this is the basis for further work in which we plan to experimentally test classical and quantum physics in many-body systems in collaboration with experimentalists.