Two--mode optical tomograms: a possible experimental check of the Robertson uncertainty relations

TL;DR

This paper proposes an experimental method using homodyne photon detection to verify two-mode Robertson uncertainty relations through optical tomograms, linking them to symplectic tomograms and quadrature dispersions.

Contribution

It introduces a novel approach to experimentally test two-mode Robertson uncertainty relations using optical tomograms and homodyne detection.

Findings

Method for checking Robertson inequalities experimentally

Connection between optical and symplectic tomograms established

Dispersion matrices linked to quadrature components

Abstract

The experimental check of two--mode Robertson uncertainty relations and inequalities for highest quadrature moments is suggested by using homodyne photon detection. The relation between optical tomograms and symplectic tomograms is used to connect the tomographic dispersion matrix and the quadrature components dispersion matrix of the two--mode field states.