{"ID":2858320,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08495","arxiv_id":"2510.08495","title":"Compiling Any $\\mathsf{MIP}^{*}$ into a (Succinct) Classical Interactive Argument","abstract":"We present a generic compiler that converts any $\\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum sub-exponential hardness of the Learning with Errors ($\\mathsf{LWE}$) problem. Prior to this work, such a compiler for $\\mathsf{MIP}^{*}$ was given by Kalai, Lombardi, Vaikuntanathan and Yang (STOC 2022), but the post-quantum soundness of this compiler is still under investigation. More generally, our compiler can be applied to any $\\mathsf{QIP}$ protocol which is sound only against semi-malicious provers that follow the prescribed protocol, but with possibly malicious initial state. Our compiler consists of two steps. We first show that if a language $\\mathcal{L}$ has a $\\mathsf{QIP}$ with semi-malicious soundness, where the prover runs in time $T$, then $\\mathcal{L} \\in \\mathsf{QMATIME}(T)$. Then we construct a succinct classical argument for any such language, where the communication complexity grows polylogarithmically with $T$, under the post-quantum sub-exponential hardness of $\\mathsf{LWE}$. Note: After this work was finished, an independent and concurrent work (Baroni et al. 2025) resolved the question of quantum soundness of the KLVY compiler.","short_abstract":"We present a generic compiler that converts any $\\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum sub-exponential hardness of the Learning with Errors ($\\mathsf{LWE}$) problem. Prior to thi...","url_abs":"https://arxiv.org/abs/2510.08495","url_pdf":"https://arxiv.org/pdf/2510.08495v2","authors":"[\"Andrew Huang\",\"Yael Tauman Kalai\"]","published":"2025-10-09T17:35:47Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.CR\"]","methods":"[]","has_code":false}