Commitments to Quantum States

Explore the concept of quantum state commitments in this 48-minute lecture by Fermi Ma from Princeton University. Delve into a novel definition of quantum state commitments (QSCs) that challenges intuition: a commitment is binding if sending it erases the committed message from the sender's perspective. Discover how this definition enables the construction of the first succinct QSCs, analogous to collision-resistant hashing for quantum messages. Examine the groundbreaking applications of QSCs, including a quantum-communication version of Kilian's succinct arguments for languages with quantum PCPs. Learn how this approach yields succinct arguments for NP under weaker assumptions than classical methods, with potential extension to QMA if the quantum PCP conjecture holds. Gain insights into a new rewinding technique for extracting quantum information, central to the security proof. Based on joint work with Sam Gunn, Nathan Ju, and Mark Zhandry, this talk offers a deep dive into the cutting-edge intersection of quantum computing and cryptography.