Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian optimizers for entropic inequalities in quantum information   We survey the state of the art for the proof of the quantum Gaussian
optimizer conjectures of quantum information theory. These fundamental
conjectures state that quantum Gaussian input states are the solution to
several optimization problems involving quantum Gaussian channels. These
problems are the quantum counterpart of three fundamental results of functional
analysis and probability: the Entropy Power Inequality, the sharp Young's
inequality for convolutions, and the theorem "Gaussian kernels have only
Gaussian maximizers." Quantum Gaussian channels play a key role in quantum
communication theory: they are the quantum counterpart of Gaussian integral
kernels and provide the mathematical model for the propagation of
electromagnetic waves in the quantum regime. The quantum Gaussian optimizer
conjectures are needed to determine the maximum communication rates over
optical fibers and free space. The restriction of the quantum-limited Gaussian
attenuator to input states diagonal in the Fock basis coincides with the
thinning, which is the analog of the rescaling for positive integer random
variables. Quantum Gaussian channels provide then a bridge between functional
analysis and discrete probability.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics