Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum information theory and Fourier multipliers on quantum groups   In this paper, we compute the exact values of the minimum output entropy and
the completely bounded minimal entropy of very large classes of quantum
channels acting on matrix algebras $\mathrm{M}_n$. Our new and incredibly
simple approach relies on the theory of locally compact quantum groups and our
results use a new and precise description of bounded Fourier multipliers from
$\mathrm{L}^1(\mathbb{G})$ into $\mathrm{L}^p(\mathbb{G})$ for $1 < p \leq
\infty$ where $\mathbb{G}$ is a co-amenable locally compact quantum group and
on the automatic completely boundedness of these multipliers that this
description entails. Indeed, our approach even allows to use multipliers on
some quantum hypergroups, notion which we define. This enable us to connect
equally the topic of computation of entropies and capacities to subfactor
planar algebras. We also give a upper bound of the classical capacity of each
considered quantum channel which is already sharp in the commutative case.
Unexpectedly, we also connect ergodic actions of (quantum) groups to this topic
of computation, allowing some some transference to other channels. Finally, we
investigate entangling breaking and $\mathrm{PPT}$ Fourier multipliers and we
characterize conditional expectations which are entangling breaking.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th