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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 Q M A. 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 * = R E in Quantum complexity. 

The class MIP^* of quantum multiprover interactive proof systems with entanglement is much more powerful than its classical counterpart MIP [Babai et al., 1991; Zhengfeng Ji et al., 2020; Zhengfeng Ji et al., 2020]: while MIP = NEXP, the quantum class MIP^* is equal to RE, a class including the halting problem. This is because the provers in MIP^* can share unbounded quantum entanglement. However, recent works [Qin and Yao, 2021; Qin and Yao, 2023] have shown that this advantage is significantly reduced if the provers' shared state contains noise. This paper attempts to exactly characterize the effect of noise on the computational power of quantum multiprover interactive proof systems. We investigate the quantum two-prover one-round interactive system MIP^*[poly,O(1)], where the verifier sends polynomially many bits to the provers and the provers send back constantly many bits. We show noise completely destroys the computational advantage given by shared entanglement in this model. Specifically, we show that if the provers are allowed to share arbitrarily many EPR states, where each EPR state is affected by an arbitrarily small constant amount of noise, the resulting complexity class is equivalent to NEXP = MIP. This improves significantly on the previous best-known bound of NEEEXP (nondeterministic triply exponential time) [Qin and Yao, 2021]. We also show that this collapse in power is due to the noise, rather than the O(1) answer size, by showing that allowing for noiseless EPR states gives the class the full power of RE = MIP^*[poly, poly]. Along the way, we develop two technical tools of independent interest. First, we give a new, deterministic tester for the positivity of an exponentially large matrix, provided it has a low-degree Fourier decomposition in terms of Pauli matrices. Secondly, we develop a new invariance principle for smooth matrix functions having bounded third-order Fréchet derivatives or which are Lipschitz continuous.