Commitments to Quantum States

Fermi Ma (Princeton University) https://simons.berkeley.edu/talks/fermi-ma-princeton-university-2023-05-05 Minimal Complexity Assumptions for Cryptography What does it mean to commit to a quantum state? In this talk, I will present a simple, but perhaps counterintuitive answer: a quantum state commitment (QSC) is binding if sending the commitment erases the committed message from the sender’s view. Using this new definition, I will show how to construct the first succinct QSCs, which can be seen as an analog of collision-resistant hashing for quantum messages. Commitments to quantum states open the door to many new cryptographic possibilities. Our flagship application is a quantum-communication version of Kilian's succinct arguments for any language that has quantum PCPs with constant error and polylogarithmic locality. Plugging in the PCP theorem, this yields succinct arguments for NP under significantly weaker assumptions than required classically; moreover, if the quantum PCP conjecture holds, this extends to QMA. At the heart of our security proof is a new rewinding technique for extracting quantum information. Joint work with Sam Gunn, Nathan Ju, and Mark Zhandry. https://eprint.iacr.org/2022/1358.pdf