Chen-Xun Weng

In many cryptographic tasks, we encounter situations where we would like to retrieve some information about two incompatible observables. A natural strategy to tackle this problem involves consecutive measurements of two observables, raising the critical question: How does the information gained from the first measurement relate to that obtained through both consecutive measurements? A loose relation between these two quantities has been established by the consecutive measurement theorem and is found useful in quantum proofs of knowledge and nonlocal games. In this work, we establish a tight consecutive measurement theorem, and apply our theorem to improve the best-known bounds on the quantum value of CHSH_q(p) games and their parallel repetition. Moreover, we explore a novel application of the consecutive measurement theorem to find tighter trade-off relations for quantum oblivious transfer in most regimes. This advancement enhances the analytical toolkit to study quantum advantage and has direct implications for quantum cryptographic protocols.