Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Qubit Separability Probabilities as Joint Functions of the Bloch
  Radii of the Qubit Subsystems   We detect a certain pattern of behavior of separability probabilities
$p(r_A,r_B)$ for two-qubit systems endowed with Hilbert-Schmidt, and more
generally, random induced measures, where $r_A$ and $r_B$ are the Bloch radii
($0 \leq r_A,r_B \leq 1$) of the qubit reduced states ($A,B$). We observe a
relative repulsion of radii effect, that is $p(r_A,r_A) < p(r_A,1-r_A)$, except
for rather narrow "crossover" intervals $[\tilde{r}_A,\frac{1}{2}]$. Among the
seven specific cases we study are, firstly, the "toy" seven-dimensional
$X$-states model and, then, the fifteen-dimensional two-qubit states obtained
by tracing over the pure states in $4 \times K$-dimensions, for $K=3, 4, 5$,
with $K=4$ corresponding to Hilbert-Schmidt (flat/Euclidean) measure. We also
examine the real (two-rebit) $K=4$, the $X$-states $K=5$, and Bures (minimal
monotone)--for which no nontrivial crossover behavior is observed--instances.
In the two $X$-states cases, we derive analytical results, for $K=3, 4$, we
propose formulas that well-fit our numerical results, and for the other
scenarios, rely presently upon large numerical analyses. The separability
probability crossover regions found expand in length (lower $\tilde{r}_A$) as
$K$ increases. This report continues our efforts (arXiv:1506.08739) to extend
the recent work of Milz and Strunz (J. Phys. A: 48 [2015] 035306) from a
univariate ($r_A$) framework---in which they found separability probabilities
to hold constant with $r_A$---to a bivariate ($r_A,r_B$) one. We also analyze
the two-qutrit and qubit-qutrit counterparts reported in arXiv:1512.07210 in
this context, and study two-qubit separability probabilities of the form
$p(r_A,\frac{1}{2})$.

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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin