Device-independent quantum cryptography beyond modularity

The security of device-independent quantum cryptography only requires the violation of a Bell inequality and makes minimal assumptions about the internal workings of the measurement devices, providing the ultimate solution to secure key exchange. However, current device-independent quantum cryptography is largely divided into 3 stages: quantum measurements, non-locality estimation, and finally classical post-processing to compute the key rate. This brings about the question of whether adopting an integrated approach to quantum cryptography would improve the rates whilst requiring less resources to be consumed. Recent successes on seedless randomness extractors act as a first step within this new integrated paradigm, opening up a wide number of possibilities for exploration. This PhD will explore quantum cryptography beyond the modularity paradigm not only by developing new techniques to jointly analyse all stages of device-independent protocols, but also by investigating how this new framework can be further improved and applied to various areas of quantum cryptography.