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Archipelagos of Total Bound and Free Entanglement | | Paul B. Slater
; | | Date: |
5 Jan 2020 | | Abstract: | First, we considerably simplify an initially quite complicated formula --
involving dilogarithms. It yields the total bound entanglement probability
($approx 0.0865542$) for a qubit-ququart ($2 imes 4$) three-parameter model,
recently analyzed for its separability properties by Li and Qiao. An
"archipelago" of disjoint bound-entangled regions appears in the space of
parameters, somewhat similarly to those recently found in our preprint, "Jagged
Islands of Bound Entanglement and Witness-Parameterized Probabilities". There,
two-qutrit and two-ququart Hiesmayr-L{"o}ffler "magic simplices" and
generalized Horodecki states had been examined. However, contrastingly, in the
present study, the entirety of bound entanglement--given by the formula
obtained--is clearly captured in the archipelago found. Further, we "upgrade"
the qubit-ququart model to a two-ququart one, for which we again find a
bound-entangled archipelago, with its total probability simply being now
$frac{1}{729} left(473-512 log left(frac{27}{16}
ight) left(1+log
left(frac{27}{16}
ight)
ight)
ight) approx 0.0890496$. Then,
"downgrading" the qubit-ququart model to a two-qubit one, we find an
archipelago of total non-bound/free entanglement probability $frac{1}{2}$. | | Source: | arXiv, 2001.1232 | | Services: | Forum | Review | PDF | Favorites | |
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