State reconstruction formulas for the s-distributions and quadratures

TL;DR

This paper develops rigorous formulas for reconstructing quantum states using s-distributions and quadratures, employing infinite matrix inversion to connect these distributions with quadrature data.

Contribution

It provides new rigorous proofs for state reconstruction formulas for s-distributions and quadratures using infinite matrix inversion.

Findings

Reconstruction formulas for Cahill-Glauber s-distributions established

Method to derive s-distributions from quadrature data demonstrated

Rigorous mathematical proofs provided for the reconstruction formulas

Abstract

We consider the method of infinite matrix inversion in the context of quantum state reconstruction. Using this method we give rigorous proofs for reconstruction formulas for the Cahill-Glauber s-parametrized distributions and the rotated quadrature distributions. We also demonstrate how to construct the s-distributions from the quadrature data.