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Article overview
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Quasirandom Estimation of Bures Two-Qubit and Two-Rebit Separability Probabilities | Paul B. Slater
; | Date: |
25 Jan 2019 | Abstract: | We employ a quasirandom methodology, recently developed by Martin Roberts, to
estimate the separability probabilities, with respect to the Bures (minimal
monotone/statistical distinguishability) measure, of generic two-qubit and
two-rebit states. This procedure, based on generalized properties of the golden
ratio, yielded, in the course of almost fifteen billion iterations, two-qubit
estimates repeatedly agreeing to close to nine decimal places with
$frac{25}{341} =frac{5^2}{11 cdot 31} approx 0.07331378299$. The
corresponding probabilities based on the Hilbert-Schmidt and operator monotone
function $sqrt{x}$ measures are (still subject to formal proof) essentially
known to be $frac{8}{33} = frac{2^3}{3 cdot 11}$ and $1-frac{256}{27
pi^2}=1-frac{4^4}{3^3 pi^2}$, respectively. Further, the analogous pair of
two-rebit probabilities has been proven by Lovas and Andai to be $frac{29}{64}
= frac{29}{2^6}$ and approximately 0.26223. In the Bures two-rebit case, we do
not presently perceive an exact value corresponding to our quasirandom estimate
of 0.15709715, based on over twenty billion iterations. The quasirandom
methodology can also be applied to test recent conjectures that the
Hilbert-Schmidt qubit-qutrit and rebit-retrit separability probabilities are
$frac{27}{1000}=frac{3^3}{2^3 cdot 5^3}$ and $frac{860}{6561}= frac{2^2
cdot 5 cdot 43}{3^8}$, respectively. | Source: | arXiv, 1901.9889 | Services: | Forum | Review | PDF | Favorites |
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