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  "path": "/abs/2604.05962v1",
  "publishedAt": "2026-04-08T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Mina Doosti",
    "Ryan Sweke",
    "Chirag Wadhwa"
  ],
  "textContent": "**Authors:** Mina Doosti, Ryan Sweke, Chirag Wadhwa\n\nWe introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $ρ$, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of $ρ$. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $σ$, decide whether $ρ=σ$ or $\\|ρ-σ\\|_1\\geq ε$. Additionally, we focus on the case of limited quantum communication between distributed nodes and the central node. We show that when each communication channel is limited to only $n_q\\leq \\log d$ qubits, then the sample complexity of distributed state certification is $\\mathcal{O}(\\frac{d^2}{2^{n_q}ε^2})$ when public randomness is available to all nodes. Moreover, under the assumption that the channels used by the distributed nodes are mixedness-preserving, we prove a matching lower bound. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $Ω(\\frac{d^3}{4^{n_q} ε^2})$ lower bound in the private-coin setting under the same assumption as above. Our lower bounds leverage a recently introduced quantum analogue of the celebrated Ingster-Suslina method and generalize arguments from the classical setting. Together, our work provides the first characterization of distributed quantum state certification in the regime of limited quantum communication and establishes a general framework for distributed quantum inference with communication constraints.",
  "title": "Distributed Quantum Property Testing with Communication Constraints"
}