Commitments to Quantum States
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What does it mean to commit to a quantum state? In this work, we propose a simple answer: a commitment to quantum messages is binding if, after the commit phase, the committed state is hidden from the sender's view. We accompany this new definition with several instantiations. We build the first non-interactive succinct quantum state commitments, which can be seen as an analogue of collision-resistant hashing for quantum messages. We also show that hiding quantum state commitments (QSCs) are implied by any commitment scheme for classical messages. All of our constructions can be based on quantum-cryptographic assumptions that are implied by but are potentially weaker than one-way functions. Commitments to quantum states open the door to many new cryptographic possibilities. Our flagship application of a succinct QSC 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.
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