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Article overview
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Octonionic two-qubit separability probability conjectures | | Paul B. Slater
; | | Date: |
8 Dec 2016 | | Abstract: | We study, further, a conjectured formula for generalized two-qubit
Hilbert-Schmidt separability probabilities that has recently been proven by
Lovas and Andai (this https URL) for its real (two-rebit)
asserted value ($frac{29}{64}$), and that has also been very strongly
supported numerically for its complex ($frac{8}{33}$), and quaternionic
($frac{26}{323}$) counterparts. Now, we seek to test the presumptive
octonionic value of $frac{44482}{4091349} approx 0.0108722$. We are somewhat
encouraged by certain numerical computations, indicating that this
(51-dimensional) instance of the conjecture might be fulfilled by setting a
certain determinantal-power parameter $a$, introduced by Forrester
(this https URL), to 0 (or possibly near to 0).
Hilbert-Schmidt measure being the case $k=0$ of random induced measure, for
$k=1$, the corresponding octonionic separability probability conjecture is
$frac{7612846}{293213345} approx 0.0259635$, while for $k=2$, it is
$frac{4893392}{95041567} approx 0.0514869, ldots$. The relation between the
parameters $a$ and $k$ is explored. | | Source: | arXiv, 1612.2798 | | Services: | Forum | Review | PDF | Favorites | |
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