Authors
Frederick Dehmel
Description
This paper examines how a qubit’s graph-theoretic degree shapes the distribution of correlations in 5-qubit graph (cluster) states across three topologies: a path, a cycle, and a star. The states are prepared using Hadamard and controlled-Z gates, after which all two-qubit reduced states are obtained via partial trace. Pairwise entanglement is quantified with concurrence and negativity, and total correlations are characterized using quantum mutual information. The study finds essentially no two-qubit entanglement in any topology, indicating genuinely multipartite entanglement, while mutual information remains non-zero, revealing substantial correlations even when bipartite entanglement measures vanish. High-degree nodes—most notably the star’s central hub—exhibit stronger distributed correlations, visualized through heatmaps and summarized with degree-dependent correlation tables.