Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitary quantum gates, perfect entanglers and unistochastic maps   Non-local properties of ensembles of quantum gates induced by the Haar
measure on the unitary group are investigated. We analyze the entropy of
entanglement of a unitary matrix U equal to the Shannon entropy of the vector
of singular values of the reshuffled matrix. Averaging the entropy over the
Haar measure on U(N^2) we find its asymptotic behaviour. For two--qubit quantum
gates we derive the induced probability distribution of the interaction content
and show that the relative volume of the set of perfect entanglers reads 8/3
\pi \approx 0.85. We establish explicit conditions under which a given
one-qubit bistochastic map is unistochastic, so it can be obtained by partial
trace over a one--qubit environment initially prepared in the maximally mixed
state.

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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an