De Finetti Structures in Networks of Quantum Systems
Abstract
Consider N identical quantum systems at the vertices of a graph, interacting via pairwise edge couplings. We designate K vertices as a system of interest S and the remaining N−K as a reservoir R. Under generic connectivity assumptions between S and R, we show that for N→∞, the reduced state of S converges to a convex combination of symmetric product states of K single-vertex density matrices -- called a de Finetti representation. Unlike in standard derivations for symmetric (exchangeable) systems, we establish de Finetti representations for quantum networks, which are inherently non-exchangeable. We construct the representations explicitly and quantify the convergence rate. We show that Erdős--Rényi random graphs exhibit the de Finetti structure: as the reservoir grows, the reduced state of any fixed finite subgraph converges almost surely to an explicit deterministic product state. As applications, we establish a general area law for the entanglement entropy of S, analyze mean-field and fluctuation scalings of the S-R interaction, and illustrate our results on qubit networks. We also derive quantitative convergence estimates for information-theoretic quantities, including von Neumann entropy, mutual information, and entanglement within S and between S and R.
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BibTeX
@misc{hull2026finetti,
title = {{De Finetti Structures in Networks of Quantum Systems}},
author = {Gavin Hull and Marco Merkli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25280},
eprint = {2610.25280},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25280},
}
RIS
TY - UNPB
TI - De Finetti Structures in Networks of Quantum Systems
AU - Gavin Hull
AU - Marco Merkli
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25280
UR - https://arxiv.org/abs/2610.25280
AB - Consider N identical quantum systems at the vertices of a graph, interacting via pairwise edge couplings. We designate K vertices as a system of interest S and the remaining N−K as a reservoir R. Under generic connectivity assumptions between S and R, we show that for N→∞, the reduced state of S converges to a convex combination of symmetric product states of K single-vertex density matrices -- called a de Finetti representation. Unlike in standard derivations for symmetric (exchangeable) systems, we establish de Finetti representations for quantum networks, which are inherently non-exchangeable. We construct the representations explicitly and quantify the convergence rate. We show that Erdős--Rényi random graphs exhibit the de Finetti structure: as the reservoir grows, the reduced state of any fixed finite subgraph converges almost surely to an explicit deterministic product state. As applications, we establish a general area law for the entanglement entropy of S, analyze mean-field and fluctuation scalings of the S-R interaction, and illustrate our results on qubit networks. We also derive quantitative convergence estimates for information-theoretic quantities, including von Neumann entropy, mutual information, and entanglement within S and between S and R.
ER -