2012/03/20 by Paul B. Slater, Slater, Paul B. · 2 citations
Mathematics · Physics and Astronomy · #33C20 #62E17 #81P40 #81P45 #FOS: Mathematics #FOS: Physical sciences #G.1.2 #G.3 #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph) #acm:33C20 #acm:62E17 #acm:81P40 #acm:81P45 #math-ph #math.MP #math.PR #msc:33C20 #msc:62E17 #msc:81P40 #msc:81P45 #quant-ph
paper · pdf · doi:10.48550/arxiv.1203.4498
11 pages, 3 figures (Fig. 3 is the titular formula); slightly modified presentation; confirmation by C. Dunkl of quaternionic (alpha =2) moment formulas for n =1, 2 also noted (p. 2)
arxiv created 2012/07/27 · arxiv updated 2012/07/30
We significantly advance the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A function P(alpha), incorporating a family of six hypergeometric functions, all with argument 27/64 =(3/4)3, is obtained here. It reproduces a series, alpha = 1/2, 1, 3/2, 2,...,32, of sixty-four Hilbert-Schmidt generic 2 x 2 generalized separability probabilities, advanced on the basis of systematic high-accuracy probability-distribution-reconstruction computations, employing 7,501 determinantal moments of partially transposed 4 x 4 density matrices. For generic (9-dimensional) two-rebit systems, P(1/2) = 29/64, (15-dimensional) two-qubit, P(1) = 8/33, and (27-dimensional) two-quat(ernionic)bit systems, P(2)= 26/323. The function P(alpha) is generated--applying the Mathematica command FindSequenceFunction--using solely either) the thirty-two integral or half-integral probabilities, yet successfully predicts the unused thirty-two.