2003/06/06 by Paul B. Slater, Slater, Paul B.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0306053
eleven pages, two tables, one figure, LaTeX, two appendices of T. Eggeling, minor changes
openalex publication_date 2003/06/06 · arxiv created 2003/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (n2-1)-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.