Succinct Arguments for QMA from Collapsing Hash Functions

Abstract:We prove the existence of succinct arguments for QMA, assuming only the existence of collapsing hash functions. This is the first scheme that relies only on unstructured ``Minicrypt'' assumptions, which are not known to imply public-key encryption. Our main technical contribution is a quantum-succinct \emph{claw-state generation} protocol that allows us to bootstrap a small number of quantum correlations into an arbitrarily large number of claw-state correlations, using classical communication only. This improves upon the work of [Zhang, STOC 2021], having better round complexity, a proof in the standard model, and being overall much simpler. This yields a quantum-succinct blind delegation of quantum computation protocol from one-way functions, which we plug into the communication-compression compiler of [Bartusek, Liu, and Malavolta, EUROCRYPT 2026] to obtain succinct arguments for QMA.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2609.35633 [quant-ph]

(or arXiv:2609.35633v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.35633 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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