Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The exact cost of redistributing multipartite quantum states   How correlated are two quantum systems from the perspective of a third? We
answer this by providing an optimal quantum state redistribution protocol for
multipartite product sources. Specifically, given an arbitrary quantum state of
three systems, where Alice holds two and Bob holds one, we identify the cost,
in terms of quantum communication and entanglement, for Alice to give one of
her parts to Bob. The communication cost gives the first known operational
interpretation to quantum conditional mutual information. The optimal procedure
is self-dual under time reversal and is perfectly composable. This generalizes
known protocols such as the state merging and fully quantum Slepian-Wolf
protocols, from which almost every known protocol in quantum Shannon theory can
be derived.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat