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.

分离观察者的测量之间的量子相关性对于随机性生成和密钥分配等应用至关重要。虽然独立于设备的安全性可以通过最小的假设进行认证，但当前协议的性能有限。在这里，我们利用以精确的时间顺序定义的顺序测量，通过重用量子态来增强性能。我们提供了几何视角和通用数学框架，分析证明了顺序量子相关性的类似 Tsirelson 的边界，这代表了顺序用户共享的非局域性的权衡。这一边界有利于安全量子随机性生成，即使一个连续用户不共享非本地性，也可以通过一个远程方和两个连续方验证每个状态的最大位数。我们的简单量子位协议达到了这个边界，数值分析表明在现实噪声下鲁棒性得到了提高。光子实现证实了可行性和鲁棒性。这项研究增进了对顺序量子相关性的理解，并为高效的设备无关协议提供了见解。