Lucio De Simone — University of Siena #
Entanglement in Graph Structures Beyond Local Connectivity #
Graph states play a central role in quantum information science, providing a unifying framework for measurement–based quantum computation, quantum error correction, and the study of many–body entanglement. When a graph structure is used to prescribe a set of pairwise interactions among qubits, the resulting state captures how the connectivity pattern influences the generation and distribution of quantum correlations. Understanding how entanglement responds to structural properties of the underlying graph is therefore of broad interest, especially when the graph is drawn from an ensemble. In this talk, I will rely on the entanglement distance, an entanglement quantifier whose geometric formulation has been summarized in [1] and recently applied to quantum systems defined on graph structures [2,3], to study graph–structured quantum states with non-local couplings induced by Katz-weighted interactions. In this setting, Katz weights encode the contribution of walks at all lengths, so that indirect connectivity, cycles, triangles and other recurrent patterns can contribute to the effective couplings. This provides a natural framework to investigate how entanglement is affected by network geometry beyond the nearest-neighbour structure encoded by the original graph. I will then apply this approach to random graph ensembles and study how the entanglement profile changes across different classes of random networks. 

[1] De Simone, L.; Capra, L.; Vesperini, A.; Rossi, L.; Di Cairano, L.; Franzosi, R. Geometric Aspects of Entanglement. Entropy 2026, 28, 299. https://doi.org/10.3390/e28030299 
[2] De Simone L and Franzosi R 2025 Journal of Physics A: Mathematical and Theoretical 58 415302 URL: https://doi.org/10.1088/1751-8121/ae0bcb 
[3] De Simone L and Franzosi R Advanced Quantum Technologies n/a e00514 (Preprint https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/qute.202500514)