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24 January 2021
  » arxiv » quant-ph/0508227

 Article overview

Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems
Paul B. Slater ;
Date 30 Aug 2005
Subject quant-ph
AbstractJakobczyk and Siennicki studied two-dimensional sections of a set of Bloch vectors corresponding to n x n density matrices of two-qubit systems (that is, the case n=4). They found essentially five different types of (nontrivial) separability regimes. We compute the Euclidean/Hilbert-Schmidt (HS) separability probabilities assigned to these regimes, and conduct parallel two-dimensional section analyses for the cases n=6,8,9 and 10. We obtain a very wide variety of exact HS-probabilities. 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, bi-PPT probabilities; and for n=8, tri-PPT 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 (one-dimensional) boundaries (both exterior and interior) of the separability and PPT domains, and discuss some exact calculations pertaining to the 9-dimensional (real) and 15-dimensional (complex) convex sets of two-qubit density matrices.
Source arXiv, quant-ph/0508227
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