Speaker
Description
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 present an explicit closed-form expression for the entanglement as a function of the underlying graph geometry [1,2]. I will first discuss explicit examples of network topologies and illustrate the application of the formula to specific graphs, highlighting its potential implications for the design of entanglement–optimized quantum networks and for graph–structured models in quantum machine learning, where controllable entanglement is a key resource. I will then extend the analysis to ensembles of graphs with statistical structure, focusing in particular on the Erdős–Rényi model. In this setting, the entanglement exhibits a phase–transition–like behavior that is distinct from the classical transition that characterizes the standard Erdős-Rényi model.
[1] 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
[2] De Simone L and Franzosi R Advanced Quantum Technologies n/a e00514 (Preprint https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/qute.202500514)