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A Dichotomy for MIP* in the Presence of Unital Noise — arXiv:2609.39318

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.39318
License (as archived): CC0-1.0
Archived: 2026-10-07T15:21:18.413Z
SHA-256 of the archived text: c3b77df82792803f0fadf640602b8db33cafac314b61d896444e8ff2e70c2514
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A Dichotomy for MIP* in the Presence of Unital Noise — arXiv:2609.39318 — arXiv (en), https://arxiv.org/abs/2609.39318 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_953fcd5deedf (Metraipolis archive dc_953fcd5deedf, sha256 c3b77df82792803f0fadf640602b8db33cafac314b61d896444e8ff2e70c2514)

BibTeX

@misc{dc953fcd5deedf,
  title = {A Dichotomy for MIP* in the Presence of Unital Noise — arXiv:2609.39318},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.39318},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_953fcd5deedf; sha256 c3b77df82792803f0fadf640602b8db33cafac314b61d896444e8ff2e70c2514},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.39318. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A recent work studied quantum two-prover one-round proof systems $\mathsf{MIP}^{\psi}[\text{poly},O(1)]$. It showed that when $\psi$ is a noisy EPR state with quantum maximal correlation $\rho_{\max}(\psi)<1$, 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 $\mathsf{MIP}^{\psi}[\text{poly},\text{poly}]$, where the provers share arbitrarily many copies of EPR pairs subject to unital noise. Equivalently, let $\psi$ be a fixed two-qubit state with maximally mixed marginals. We prove that \[\mathsf{MIP}^{\psi}[\text{poly},\text{poly}]=\mathsf{MIP} =\mathsf{NEXP},~\text{if $\psi$ is separable or $\rho_{\max}(\psi)<1$};\]\[\mathsf{MIP}^{\psi}[\text{poly},\text{poly}]=\mathsf{MIP}^{\psi}[\text{poly},O(1)]=\mathsf{RE},\text{if $\psi$ is entangled and $\rho_{\max}(\psi)=1$.}\] 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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-01 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.39318 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T14:53:56.675Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).