Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-local properties of multi-particle density matrices   As far as entanglement is concerned, two density matrices of $n$ particles
are equivalent if they are on the same orbit of the group of local unitary
transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of
particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal
to two, the number of independent parameters needed to specify an $n$-particle
density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For
$n$ spin-${1\over 2}$ particles we also show how to characterise generic
orbits, both by giving an explicit parametrisation of the orbits and by finding
a finite set of polynomial invariants which separate the orbits.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
17
The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org