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What does it mean to commit to a quantum state? In this work, we propose asimple answer: a commitment to quantum messages is binding if, after the commitphase, the committed state is hidden from the sender's view. We accompany thisnew definition with several instantiations. We build the first non-interactivesuccinct quantum state commitments, which can be seen as an analogue ofcollision-resistant hashing for quantum messages. We also show that hidingquantum state commitments (QSCs) are implied by any commitment scheme forclassical messages. All of our constructions can be based onquantum-cryptographic assumptions that are implied by but are potentiallyweaker than one-way functions.  Commitments to quantum states open the door to many new cryptographicpossibilities. Our flagship application of a succinct QSC is aquantum-communication version of Kilian's succinct arguments for any languagethat has quantum PCPs with constant error and polylogarithmic locality.Plugging in the PCP theorem, this yields succinct arguments for NP undersignificantly weaker assumptions than required classically; moreover, if thequantum PCP conjecture holds, this extends to QMA. At the heart of our securityproof is a new rewinding technique for extracting quantum information.

Commitments to Quantum States