Chen-Xun Weng

In many quantum information tasks, we encounter scenarios where information about two incompatible observables must be retrieved. A natural approach is to perform consecutive measurements, raising a key question: How does the information gained from the first measurement compare to that from both? The consecutive measurement theorem (CMT) provides a general relation between these quantities and has found applications in quantum cryptography. However, its previous formulations are often either too loose or too brittle to yield meaningful bounds. In this work, we first establish a tight CMT and apply it to achieve the best upper bounds on the quantum value of certain nonlocal games and their parallel repetitions to date. We then develop a robust CMT and explore a novel application of CMT to obtain a tighter no-go theorem for quantum oblivious transfer in some regime. These contributions strengthen the theoretical tools for analyzing quantum advantage and have concrete implications for nonlocal games and quantum cryptographic protocols.

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.