Ilya Merkulov

In device-independent (DI) quantum protocols, the security statements are oblivious to the characterization of the quantum apparatus– they are based solely on the classical interaction with the devices as well as some well-defined assumptions. The most commonly known setup is the so-called non-local one, in which two devices that cannot communicate with each other present a violation of a Bell inequality. In recent years, a new variant of DI protocols, requiring only a single device, arose. In this novel research avenue, the no-communication assumption is replaced with a computational assumption which states that the device cannot solve certain post-quantum cryptographic tasks. The protocols in literature that have been analyzed in this setting, e.g., randomness certification, used ad hoc proof techniques. In addition, the strength of the achieved results is hard to judge due to their complexity. Here, we build on ideas coming from the study of non-local DI protocols and develop a new modular proof technique for the single-device computational setting. We present a flexible framework for proving the security of such protocols by utilizing a combination of tools from quantum information theory, such as the entropic uncertainty relation and the entropy accumulation theorem. This leads to an insightful and simple proof of security as well as to explicit quantitative bounds. Our work thus acts as the basis for the analysis of future protocols for DI randomness generation, expansion, amplification, and key distribution based on post-quantum cryptographic assumptions.