Tight and Robust Consecutive Measurement Theorems with Applications to Quantum Cryptography
Chen-Xun Weng (Nanjing University); Minglong Qin (National University of Singapore); Yanglin Hu (University of Hong Kong); Marco Tomamichel (National University of Singapore)
[abstract]Abstract: 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.
