Yanglin Hu

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.

Weak coin flipping is a cryptographic primitive in which two mutually distrustful parties generate a shared random bit to agree on a winner via remote communication. While a stand-alone secure weak coin flipping protocol can be constructed from noiseless communication channels, its composability has not been explored. In this work, we demonstrate that no weak coin flipping protocol can be abstracted into a black box resource with composable security. Despite this, we also establish the overall stand-alone security of weak coin flipping protocols under sequential composition.

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.

The no-cloning theorem is a cornerstone of quantum cryptography. Here we generalize and rederive under weaker assumptions various upper bounds on the maximum achievable fidelity of probabilistic and deterministic cloning machines. Building on ideas by Gisin [Phys.~Lett.~A, 1998], our results hold even for cloning machines that do not obey the laws of quantum mechanics, as long as remote state preparation is possible and the non-signalling principle holds. We apply our general theorem to several subsets of states that are of interest in quantum cryptography.