Archipelagos of Total Bound and Free Entanglement

• URL: http://arxiv.org/abs/2001.01232v1
• Date: Sun, 5 Jan 2020 13:19:31 GMT
• Title: Archipelagos of Total Bound and Free Entanglement
• Authors: Paul B. Slater
• Abstract summary: We simplify an initially quite complicated formula involving dilogarithms. We find an archipelago of total non-bound/free entanglement probability $frac1729 left(473-512 log left(frac2716right)right approx 0.0890496$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 ($2 \times 4$) 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 $\frac{1}{729} \left(473-512 \log \left(\frac{27}{16}\right) \left(1+\log \left(\frac{27}{16}\right)\right)\right) \approx 0.0890496$. Then, "downgrading" the qubit-ququart model to a two-qubit one, we find an archipelago of total non-bound/free entanglement probability $\frac{1}{2}$.

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