Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating quantum channels by completely positive maps with small
  Kraus rank   We study the problem of approximating a quantum channel by one with as few
Kraus operators as possible (in the sense that, for any input state, the output
states of the two channels should be close to one another). Our main result is
that any quantum channel mapping states on some input Hilbert space
$\mathrm{A}$ to states on some output Hilbert space $\mathrm{B}$ can be
compressed into one with order $d\log d$ Kraus operators, where
$d=\max(|\mathrm{A}|,|\mathrm{B}|)$, hence much less than
$|\mathrm{A}||\mathrm{B}|$. In the case where the channel's outputs are all
very mixed, this can be improved to order $d$. We discuss the optimality of
this result as well as some consequences.

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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat