Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity Properties of Certain Measures over the Two-Level Quantum
  Systems   We demonstrate --- using the case of the two-dimensional quantum systems ---
that the "natural measure on the space of density matrices describing
N-dimensional quantum systems" proposed by Zyczkowski et al (quant-ph/9804024)
does not belong to the class of normalized volume elements of monotone metrics
on the quantum systems. Such metrics possess the statistically important
property of being decreasing under stochastic mappings (coarse-grainings). We
do note that the proposed natural measure (and certain evident variations upon
it) exhibit quite specific monotonicity properties, but not of the form
required for membership in the class.

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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga