2004/06/30 by Samuel L. Braunstein, Sibasish Ghosh, Simone Severini · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Graph theory and applications #Quantum Computing Algorithms and Architecture #Quantum many-body systems #math.CO #quant-ph
paper · pdf · doi:10.1007/s00026-006-0289-3
published as Annals of Combinatorics, Volume 10, No 3, 2006 · 20 pages, 11 figures
arxiv created 2006/10/09 · openalex publication_date 2006/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graph on four vertices representing entangled states. It turns out that for some of these graphs the value of the concurrence is exactly fractional.