2006/02/28 by Ali Saif M. Hassan, Pramod S. Joag, Pramod Joag · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Mathematics #Multipartite #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Theoretical computer science #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/33/019
published as J. Phys. A: Math. Theor. 40 (2007) 10251--10290 · 55 pages,24 figures. Comments are welcome
arxiv created 2007/06/18 · openalex publication_date 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study related issues such as classification of pure and mixed states, Von Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum states. In order to address the separability and entanglement questions using graphs, we introduce a modified tensor product of weighted graphs, and establish its algebraic properties. In particular, we show that Werner's definition (Werner 1989 Phys. Rev. A 40 4277) of a separable state can be written in terms of graphs, for the states in a real or complex Hilbert space. We generalize the separability criterion (degree criterion) due to Braunstein et al (2006 Phys. Rev. A 73 012320) to a class of weighted graphs with real weights. We have given some criteria for the Laplacian associated with a weighted graph to be positive semidefinite.