Neural networks learn to reconstruct multipartite entanglement from quantum marginals
Abstract
Different sets of local correlations are not equivalent: some fragments of reduced data uniquely determine a global quantum state, while others leave it ambiguous. The quantum marginal problem asks whether a collection of reduced density matrices uniquely determines a compatible global quantum state. Although generic quantum states are uniquely specified by suitable sets of marginals, different collections of marginals are not equally informative: some uniquely determine the global state, whereas others leave it ambiguous. Identifying when uniqueness holds, and reconstructing the global state from partial information, remains computationally demanding and experimentally challenging. We show that information about the multipartite entanglement class and reconstructability in four-qubit systems is compactly encoded in small sets of two- and three-qubit marginals. Using semidefinite programming, we chart the reconstructability landscape across 49 inequivalent SLOCC entanglement classes and show that uniqueness strongly depends on both entanglement structure and marginal order. Neural networks trained only on reduced density matrices learn this structure directly. They accurately classify marginal reconstructability and, when uniqueness holds, reconstruct the full four-qubit density matrix with high fidelity from two- and three-qubit marginals. We benchmark the approach on a four-qubit nuclear magnetic resonance quantum processor and demonstrate that reconstructions from experimentally measured marginals remain faithful despite phase damping and control imperfections. Our results show that neural networks can learn when local correlations uniquely specify a global quantum state, and reveal how global quantum structure is encoded in reduced data.
Related
- Optimising multipartite entanglement manipulation in quantum networks
- Neural network-based multipartite entanglement classification with prior guidance from quantum uncertainty relations
- Quantum Fisher Information as the Speed Limit for Multipartite Entanglement
- Nonlocality without entanglement for multipartite quantum measurements
- Predicting Multipartite Entanglement in Quantum Circuits using Transformer
BibTeX
@misc{kandpal2026neural,
title = {{Neural networks learn to reconstruct multipartite entanglement from quantum marginals}},
author = {Matreyee Kandpal and Arvind and Kavita Dorai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04896},
eprint = {2609.04896},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04896},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Neural networks learn to reconstruct multipartite entanglement from quantum marginals
AU - Matreyee Kandpal
AU - Arvind
AU - Kavita Dorai
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04896
UR - https://arxiv.org/abs/2609.04896
AB - Different sets of local correlations are not equivalent: some fragments of reduced data uniquely determine a global quantum state, while others leave it ambiguous. The quantum marginal problem asks whether a collection of reduced density matrices uniquely determines a compatible global quantum state. Although generic quantum states are uniquely specified by suitable sets of marginals, different collections of marginals are not equally informative: some uniquely determine the global state, whereas others leave it ambiguous. Identifying when uniqueness holds, and reconstructing the global state from partial information, remains computationally demanding and experimentally challenging. We show that information about the multipartite entanglement class and reconstructability in four-qubit systems is compactly encoded in small sets of two- and three-qubit marginals. Using semidefinite programming, we chart the reconstructability landscape across 49 inequivalent SLOCC entanglement classes and show that uniqueness strongly depends on both entanglement structure and marginal order. Neural networks trained only on reduced density matrices learn this structure directly. They accurately classify marginal reconstructability and, when uniqueness holds, reconstruct the full four-qubit density matrix with high fidelity from two- and three-qubit marginals. We benchmark the approach on a four-qubit nuclear magnetic resonance quantum processor and demonstrate that reconstructions from experimentally measured marginals remain faithful despite phase damping and control imperfections. Our results show that neural networks can learn when local correlations uniquely specify a global quantum state, and reveal how global quantum structure is encoded in reduced data.
ER -