Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Von Neumann entropy and majorization   We consider the properties of the Shannon entropy for two probability
distributions which stand in the relationship of majorization. Then we give a
generalization of a theorem due to Uhlmann, extending it to infinite
dimensional Hilbert spaces. Finally we show that for any quantum channel
$\Phi$, one has $S(\Phi(\rho))=S(\rho)$ for all quantum states $\rho$ if and
only if there exists an isometric operator $V$ such that $\Phi(\rho)=V\rho
V^*$.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int