Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States
Previously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ) and their partial transposes (|ρPT|), was applied with k=0 to the generalized two-qubit separability probability question. The formula can,...
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/621353 |
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| author | Paul B. Slater Charles F. Dunkl |
| author_facet | Paul B. Slater Charles F. Dunkl |
| author_sort | Paul B. Slater |
| collection | DOAJ |
| description | Previously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ) and their partial transposes (|ρPT|), was applied with k=0 to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,…) are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2), (standard) two-qubit (α=1), and two-quater[nionic]bit (α=2) cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed for general k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula. |
| format | Article |
| id | doaj-art-1058ba9ae4174a7a8849b026b43ee628 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-1058ba9ae4174a7a8849b026b43ee6282025-02-03T00:59:01ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/621353621353Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit StatesPaul B. Slater0Charles F. Dunkl1University of California, Santa Barbara, Santa Barbara, CA 93106-4030, USADepartment of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USAPreviously, a formula, incorporating a 5F4 hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments ρPTnρk/ρk of 4×4 density-matrices (ρ) and their partial transposes (|ρPT|), was applied with k=0 to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,…) are found—via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2), (standard) two-qubit (α=1), and two-quater[nionic]bit (α=2) cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed for general k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.http://dx.doi.org/10.1155/2015/621353 |
| spellingShingle | Paul B. Slater Charles F. Dunkl Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States Advances in Mathematical Physics |
| title | Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States |
| title_full | Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States |
| title_fullStr | Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States |
| title_full_unstemmed | Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States |
| title_short | Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States |
| title_sort | formulas for rational valued separability probabilities of random induced generalized two qubit states |
| url | http://dx.doi.org/10.1155/2015/621353 |
| work_keys_str_mv | AT paulbslater formulasforrationalvaluedseparabilityprobabilitiesofrandominducedgeneralizedtwoqubitstates AT charlesfdunkl formulasforrationalvaluedseparabilityprobabilitiesofrandominducedgeneralizedtwoqubitstates |