Bures/statistical distinguishability probabilities of triseparable and biseparable Eggeling-Werner States
Abstract
In a number of previous studies, we have investigated the use of the volume element of the Bures (minimal monotone) metric -- identically, one-fourth of the statistical distinguishability (SD) metric -- as a natural measure over the (n^2-1)-dimensional convex set of n x n density matrices. This has led us for the cases n = 4 and 6 to estimates of the prior (Bures/SD) probabilities that qubit-qubit and qubit-qutrit pairs are separable. Here, we extend this work from such bipartite systems to the tripartite "laboratory'' quantum systems possessing U x U x U symmetry recently constructed by Eggeling and Werner (Phys. Rev. A 63 [2001], 042324). We derive the associated SD metric tensors for the three-qubit and three-qutrit cases, and then obtain estimates of the various related Bures/SD probabilities using Monte Carlo methods.
Keywords
Cite
@article{arxiv.quant-ph/0306053,
title = {Bures/statistical distinguishability probabilities of triseparable and biseparable Eggeling-Werner States},
author = {Paul B. Slater},
journal= {arXiv preprint arXiv:quant-ph/0306053},
year = {2007}
}
Comments
eleven pages, two tables, one figure, LaTeX, two appendices of T. Eggeling, minor changes