An important drawback in many conventional quantum information protocols is that they require an experimenter to flawlessly control their laboratory. This is an idealization that one may only aspire to meet. For all practical purposes, quantum devices cannot be fully controlled. A powerful solution is called device-independence. In contrast to conventional protocols, device-independent protocols view quantum devices as black boxes, i.e. systems about which we know nothing. The success of a protocol is then deduced only from the statistics produced by these black boxes. However, such minimalistic assumptions make implementations very demanding.
This has motivated a semi-device-independent approach, where one aims to combine the black-box spirit of device-independence with the friendliness in implementation of conventional protocols. To achieve this, one makes only a small and reasonable assumption on the quantum devices. The natural question therefore becomes: what assumption should we make? The answer that has dominated research on the topic in the last decade has been to assume knowledge of the relevant degrees of freedom, i.e. the quantum dimension. This approach has harvested much success, but it has well-known drawbacks: dimensions cannot be measured and they cannot be controlled in each round of an experiment.
The newly published paper proposes to substitute the dimension-assumption for something entirely different, namely an assumption of a lower limit on the quality of a quantum device. The idea is to first let the experimenter decide which procedure to run in their lab and then estimate how inaccurately this procedure possibly could be performed, i.e. how much the device should be distrusted. This estimation can be based on a measurable quantity and describes the experiment on the level of probabilities, rather than on a round-to-round basis. The work establishes methods to characterize quantum correlations when the distrust is bounded and also shows how this understanding can be harvested for the development of concrete quantum information protocols e.g. for certification of detection efficiency or the generation of random numbers. In this picture, one can investigate the trade-off between weaker assumptions (more distrust) and the efficiency of quantum information protocols.