Succinct arguments for QMA from standard assumptions via compiled nonlocal games

TL;DR

This paper presents a new, simpler way to create succinct classical arguments for QMA using only standard cryptographic assumptions, avoiding complex primitives previously thought necessary.

Contribution

It introduces a construction of a succinct classical argument system for QMA based on weaker, standard cryptographic assumptions, utilizing a general transformation for quantum nonlocal games.

Findings

Constructed a succinct classical argument system for QMA from standard assumptions.

Analyzed the soundness of a transformation applied to a quantum self-test for Pauli measurements.

Achieved a protocol that relies on collapsing hash functions and quantum homomorphic encryption.

Abstract

We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTO '22) also constructed a succinct classical argument system for QMA. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP*=RE in quantum complexity.