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A Concise Formula for Generalized Two-Qubit Hilbert-Schmidt Separability Probabilities | Paul B. Slater
; | Date: |
28 Jan 2013 | Abstract: | We report major advances in 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. It reproduces a series, alpha = 1/2, 1, 3/2,...,32 of
sixty-four conjectured Hilbert-Schmidt rational-valued generic 2 x 2
separability probabilities. These exact ratios are put forth on the basis of
systematic, high-accuracy probability-distribution-reconstruction computations,
employing 7,501 determinantal moments of partially transposed 4 x 4 density
matrices. A lengthy expression for P(alpha) containing six generalized
hypergeometric functions is initially obtained--making use of the
FindSequenceFunction command of Mathematica. A remarkably succinct
re-expression for P(alpha) is then found, by Qing-Hu Hou and colleagues, using
Zeilberger’s algorithm ("creative telescoping"), For generic (9-dimensional)
two-rebit systems, P(1/2}) = 29/64, (15-dimensional) two-qubit, P(1) = 8/33 (a
value that had been proposed in J. Phys. A, 40, 14279 [2007] and supported in
Intl. J. Mod. Phys. B, 26, 1250054 [2012]) and (27-dimensional)
two-quater(nionic)bit systems, P(2)=26/323. | Source: | arXiv, 1301.6617 | Services: | Forum | Review | PDF | Favorites |
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