Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch Radii Repulsion in Separable Two-Qubit Systems   Milz and Strunz recently reported substantial evidence to further support the
previously conjectured separability probability of $\frac{8}{33}$ for two-qubit
systems ($\rho$) endowed with Hilbert-Schmidt measure. Additionally, they found
that along the radius ($r$) of the Bloch ball representing either of the two
single-qubit subsystems, this value appeared constant (but jumping to unity at
the locus of the pure states, $r=1$). Further, they also observed (personal
communication) such separability probability $r$-invariance, when using, more
broadly, random induced measure ($K=3,4,5,\ldots$), with $K=4$ corresponding to
the (symmetric) Hilbert-Schmidt case. Among the findings here is that this
invariance is maintained even after splitting the separability probabilities
into those parts arising from the determinantal inequality $|\rho^{PT}|
>|\rho|$ and those from $|\rho| > |\rho^{PT}| >0$, where the partial transpose
is indicated. The nine-dimensional set of generic two-re[al]bit states endowed
with Hilbert-Schmidt measure is also examined, with similar $r$-invariance
conclusions. Contrastingly, two-qubit separability probabilities based on the
Bures (minimal monotone) measure {\it diminish} with $r$. Moreover, we study
the forms that the separability probabilities take as joint (bivariate)
functions of the radii ($r_A, r_B$) of the Bloch balls of {\it both}
single-qubit subsystems. Here, a form of Bloch radii {\it repulsion} for
separable two-qubit systems emerges in {\it all} our several analyses.
Separability probabilities tend to be smaller when the lengths of the two radii
are closer. In Appendix A, we report certain companion analytic results for the
much-investigated, more amenable (7-dimensional) $X$-states model.

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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th