Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All Moments of the Uniform Ensemble of Quantum Density Matrices   Given a uniform ensemble of quantum density matrices $\rho$, it is useful to
calculate the mean value over this ensemble of a product of entries of $\rho$.
We show how to calculate such moments in this paper. The answer involves well
known results from Group Representation Theory and Random Matrix Theory. This
quantum problem has a well known classical counterpart: given a uniform
ensemble of probability distributions $P=(P_1, P_2, ..., P_N)$ where the $P_j$
are non-negative reals that sum to one, calculate the mean value over this
probability simplex of products of $P$ components. The answer to the classical
problem follows from an integral formula due to Dirichlet.

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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th