{
  "abstract": "A recent work studied quantum two-prover one-round proof systems $\\mathsf{MIP}^ψ[\\text{poly},O(1)]$. It showed that when $ψ$ is a noisy EPR state with quantum maximal correlation $ρ_{\\max}(ψ)<1$, the resulting complexity class is equivalent to $\\mathsf{NEXP}=\\mathsf{MIP}$. In contrast, $\\mathsf{MIP}^{\\text{EPR}}[\\text{poly},O(1)]=\\mathsf{RE}$. Not all noise, however, decreases quantum maximal correlation. A basic example is dephasing noise: a dephased EPR pair retain quantum maximal correlation $1$. In this work, we remove the constant-answer restriction and establish a complete dichotomy for $\\mathsf{MIP}^ψ[\\text{poly},\\text{poly}]$, where the provers share arbitrarily many copies of EPR pairs subject to unital noise. Equivalently, let $ψ$ be a fixed two-qubit state with maximally mixed marginals. We prove that \\[\\mathsf{MIP}^ψ[\\text{poly},\\text{poly}]=\\mathsf{MIP} =\\mathsf{NEXP},~\\text{if $ψ$ is separable or $ρ_{\\max}(ψ)<1$};\\]\\[\\mathsf{MIP}^ψ[\\text{poly},\\text{poly}]=\\mathsf{MIP}^ψ[\\text{poly},O(1)]=\\mathsf{RE},\\text{if $ψ$ is entangled and $ρ_{\\max}(ψ)=1$.}\\] Beyond the complexity classification, our proof develops two techniques that may be useful more broadly in quantum information and quantum complexity. First, we introduce a positivity-preserving low-degree approximation framework for quantum measurements: instead of truncating positive operators directly in the Pauli basis, we approximate suitable square-root factorizations, simultaneously achieving low Pauli degree, positivity, and global control over an entire POVM. Second, we develop a new dimension-reduction method, called Pauli folding, for low-degree positive operators. Its key ingredient is an almost-multiplicativity theorem for randomized Pauli hashing, which allows noncommutative products, positivity, and normalization to survive compression with controlled error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39318",
  "author_total": 5,
  "authors": [
    {
      "name": "Yangjing Dong"
    },
    {
      "name": "Zhenyu Jiang"
    },
    {
      "name": "Minglong Qin"
    },
    {
      "name": "Penghui Yao"
    },
    {
      "name": "Haigang Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6ka9f91e8d7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39318",
  "fulltext_url": null,
  "id": "d6ka9f91e8d7e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39318",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7215123602",
  "pdf_url": "https://arxiv.org/pdf/2609.39318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6ka9f91e8d7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39318"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Dichotomy for MIP* in the Presence of Unital Noise",
  "title_text": "A Dichotomy for MIP* in the Presence of Unital Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/d6ka9f91e8d7e",
  "venue": "arXiv",
  "versions": []
}