Matteo Padovan

Quantum correlations between measurements of two or more separated observers play a fundamental role in many applications, such as randomness generation or key distribution. Although security can be certified from correlations with minimal assumptions in the device-independent scenario, the performance of such protocols is currently limited. This limitation motivates the exploration of sequential measurements, that is, defined with precise temporal ordering, as a means of improving performance through the reuse of the quantum states. To date, the study of sequential quantum protocols has been modest, lacking a comprehensive mathematical framework to explore the properties of the obtainable correlations. In this study, we adopt a geometric perspective to investigate sequential quantum correlations, providing a general mathematical framework. Here, we analytically prove a Tsirelson-like boundary for sequential quantum correlations, expressed as a trade-off between the amount of nonlocality shared by each sequential user. This boundary is particularly beneficial for the generation of secure quantum randomness. Indeed, observing a correlation on it can certify the maximum attainable bits per state in the case of one remote party and two sequential parties. In contrast to all previous schemes, this can happen even if one of the sequential users does not share any nonlocality. We demonstrate that this quantum boundary can be reached with a simple qubit protocol and investigate numerically the robustness of randomness generation under realistic noise conditions, finding that it greatly improved compared to previous proposals. Our proof-of-concept photonic implementation of the protocol confirms experimentally that our approach certifies more bits per state compared to the standard Clauser-Horne-Shimony-Holt scenario for the same noise, affirming both feasibility and robustness. This study marks a significant advance in understanding sequential quantum correlations, offering valuable insights and new mathematical tools for further fundamental studies and practical applications of efficient device-independent protocols.