A proof for the informational completeness of the rotated quadrature observables

TL;DR

This paper provides a rigorous proof that rotated quadrature observables over a dense subset of angles form an informationally complete set for single mode electromagnetic fields, enhancing understanding of quantum measurement completeness.

Contribution

It offers a new mathematically rigorous proof establishing the informational completeness of rotated quadrature observables over dense angle subsets.

Findings

Rotated quadrature operators over dense subsets are informationally complete.

The proof solidifies the theoretical foundation for quantum state reconstruction.

Enhances the mathematical understanding of quantum measurement completeness.

Abstract

We give a new mathematically rigorous proof for the fact that, when $S$ is a dense subset of $[0,2\pi)$, the rotated quadrature operators $Q_\theta$, $\theta\in S$, of a single mode electromagnetic field constitute an informationally complete set of observables.