0 Ju l 2 00 6 Combinatorial Laplacians and Positivity Under Partial Transpose
نویسندگان
چکیده
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). This work deals with properties of density matrices of graphs and indicates some venues for future research in this subject. Namely, we prove that the condition called degree-criterion, which was conjectured to be necessary and sufficient for separability of density matrices of graphs, is equivalent to the PPT-criterion. Additionally, we give an alternative proof of the sufficiency of the degree-criterion when one of the subsystems has dimension two (see Wu, Phys. Lett. A 351 [email protected] [email protected] [email protected]
منابع مشابه
N ov 2 00 6 Combinatorial Laplacians and Positivity Under Partial Transpose
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can be considered. We prove that the so-called degree-criterion, which was conjectured to be necessa...
متن کاملCombinatorial laplacians and positivity under partial transpose
ROLAND HILDEBRAND†, STEFANO MANCINI‡ and S IMONE SEVERINI§¶ †LJK Université Joseph Fourier, Tour IRMA, 51 rue des Mathématiques, 38400 St. Martin d’Hères, France ‡Dipartimento di Fisica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy §Department of Computer Science, University of York, Heslington, Y010 5DD York, United Kingdom ¶Current address: Institute for Quantum ...
متن کامل2 4 Ju l 2 00 7 INVARIANT METRICS AND LAPLACIANS ON SIEGEL - JACOBI SPACE
In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.
متن کاملv 1 1 3 Ju l 2 00 0 Twist Positivity for Lagrangian Symmetries ∗
We prove twist positivity and positivity of the pair correlation function for combined spatial and internal symmetries of free bosonic Lagrangians. We work in a general setting, extending the results obtained in Twist Positivity [1]. Work supported in part by the Department of Energy under Grant DE-FG02-94ER-25228. This research was carried out in part for the Clay Mathematics Institute.
متن کامل0 10 70 26 v 1 2 6 Ju l 2 00 1 Combinatorial identities for binary necklaces from exact ray - splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (Pólya necklaces).
متن کامل