2012/11/12 by Paul B. Slater, Slater, Paul B.
Mathematics · Physics and Astronomy · #33C20 #62E17 #81P40 #81P45 #Advanced Statistical Methods and Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph) #Random Matrices and Applications #Statistical Mechanics and Entropy #math-ph #math.MP #math.PR #msc:33C20 #msc:62E17 #msc:81P40 #msc:81P45 #quant-ph
paper · pdf · doi:10.48550/arxiv.1211.2784
15 pages, 10 figures (five of them, Mathematica output)
arxiv created 2012/11/12 · openalex publication_date 2012/11/12 · arxiv updated 2012/11/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We attempt to construct the exact univariate probability distributions for 2 x 2 quantum systems that yield the (balanced) univariate Hilbert-Schmidt determinantal moments <(|rho| |rhoPT|)n>, obtained by Slater and Dunkl (J. Phys. A, 45, 095305 [2012]). To begin, we follow--to the extent possible--the Mellin transform-based approach of Penson and Zyczkowski in their study of Fuss-Catalan and Raney distributions (Phys. Rev. E, 83, 061118 [2011]). Further, we approximate the y-intercepts (separability/entanglement boundaries)--at which |rhoPT|=0-- of the associated probability distributions based on the (balanced) moments, as well as the previously reported unbalanced determinantal moments <|rhoPT|n>, as a function of the seventy-two values of the Dyson-index-like parameter alpha = 1/2 (rebits), 1 (qubits),...,2 (quaterbits),...35.