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A pair of quasirandom estimations of two-qubit separability probabilities with respect to ten measures -- the Hilbert-Schmidt and nine operator monotone ones | | Paul B. Slater
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17 Oct 2019 | | Abstract: | We conduct a pair of quasirandom estimations of the separability
probabilities with respect to ten measures on the 15-dimensional convex set of
two-qubit states, using its Euler-angle parameterization. The measures include
the (non-monotone) Hilbert-Schmidt one, plus nine based on operator monotone
functions. Our results are supportive of previous assertions that the
Hilbert-Schmidt and Bures (minimal monotone) separability probabilities are
$frac{8}{33} approx 0.242424$ and $frac{25}{341} approx 0.0733138$,
respectively, as well as suggestive of the Wigner-Yanase counterpart being
$frac{1}{20}$. However, they appear inconsistent (much too small) with the
additional claim that the separability probability associated with the operator
monotone (geometric-mean) function $sqrt{x}$ is $1-frac{256}{27 pi ^2}
approx 0.0393251$. But a seeming explanation for this phenomenon is that the
volume of states for the $sqrt{x}$-based measure is infinite, so the validity
of the conjecture--as well as an alternative one, $frac{1}{9} left(593-60 pi
^2
ight) approx 0.0915262$, we now introduce--can not be examined through our
numerical approach, at least perhaps not without some truncation procedure for
extreme values. | | Source: | arXiv, 1910.7937 | | Services: | Forum | Review | PDF | Favorites | |
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