In continuous-variable quantum information processing, error correction of Gaussian errors requires simultaneous estimation both quadrature components displacements on phase space. However, operators $x$ and $p$ are non-commutative conjugate observables, whose measurement is prohibited by the uncertainty principle. Gottesman-Kitaev-Preskill (GKP) deals with this problem using complex non-Gaussi...

The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the paraxial approximation. Here, a different technique is presented: Using the plane wave representation of the fundamental Gaussian mode as seed function, all...

Measures of quantum properties are essential to understanding the fundamental differences between and classical systems as well quantifying resources for technologies. Here two broad classes bosonic phase-space functions, which filtered versions Glauber-Sudarshan $P$ function, compared with regard their ability uncover nonclassical effects light through negativities. Gaussian filtering function...