ua nt - p h / 06 02 05 3 v 4 12 J ul 2 00 6 Combinatorial approach to multipartite quantum systems : basic formulation

نویسندگان

  • Ali Saif M. Hassan
  • Pramod Joag
چکیده

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 the related issues like 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 particular, we give a necessary and sufficient criterion for a m-partite quantum state to be separable. We generalize the separability criterion due to Braunstein, Ghosh and Severini to a class of weighted graphs with real or complex weights. We have given some criteria for the Laplacian associated with a graph to be positive semidefinite.

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تاریخ انتشار 2006