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HilbertSchmidt Geometry of nLevel JakobczykSiennicki TwoDimensional Quantum Systems  Paul B. Slater
;  Date: 
30 Aug 2005  Subject:  quantph  Abstract:  Jakobczyk and Siennicki studied twodimensional sections of a set of Bloch vectors corresponding to n x n density matrices of twoqubit systems (that is, the case n=4). They found essentially five different types of (nontrivial) separability regimes. We compute the Euclidean/HilbertSchmidt (HS) separability probabilities assigned to these regimes, and conduct parallel twodimensional section analyses for the cases n=6,8,9 and 10. We obtain a very wide variety of exact HSprobabilities. For n>6, the probabilities are those of having a partial positive transpose (PPT). For the n=6 case, we also obtain biseparability probabilities; in the n=8,9 instances, biPPT probabilities; and for n=8, triPPT probabilities. By far, the most frequently recorded probability for n>4 is Pi/4 = 0.785398$. We also conduct a number of related analyses, pertaining to the (onedimensional) boundaries (both exterior and interior) of the separability and PPT domains, and discuss some exact calculations pertaining to the 9dimensional (real) and 15dimensional (complex) convex sets of twoqubit density matrices.  Source:  arXiv, quantph/0508227  Services:  Forum  Review  PDF  Favorites 


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