Secure and robust randomness with sequential quantum measurements

Quantum correlations between measurements of separated observers are crucial for applications like randomness generation and key distribution. Although device-independent security can be certified with minimal assumptions, current protocols have limited performance. Here, we exploit sequential measurements, defined with a precise temporal order, to enhance performance by reusing quantum states. We provide a geometric perspective and a general mathematical framework, analytically proving a Tsirelson-like boundary for sequential quantum correlations, which represents a trade-off in nonlocality shared by sequential users. This boundary is advantageous for secure quantum randomness generation, certifying maximum bits per state with one remote and two sequential parties, even if one sequential user shares no nonlocality. Our simple qubit protocol reaches this boundary, and numerical analysis shows improved robustness under realistic noise. A photonic implementation confirms feasibility and robustness. This study advances the understanding of sequential quantum correlations and offers insights for efficient device-independent protocols.